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The Brunn-Minkowski Inequality and a Minkowski Problem for Nonlinear Capacity
| The Brunn-Minkowski Inequality and a Minkowski Problem for Nonlinear Capacity |
| Autore | Akman Murat |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 2022 |
| Descrizione fisica | 1 online resource (128 pages) |
| Disciplina |
515/.3533
515.3533 |
| Altri autori (Persone) |
GongJasun
HinemanJay |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Minkowski geometry
Inequalities (Mathematics) Nonlinear theories Elliptic functions Harmonic functions Partial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations Potential theory -- Higher-dimensional theory -- Potentials and capacities, extremal length Difference and functional equations -- Functional equations and inequalities -- Functional inequalities, including subadditivity, convexity, etc Convex and discrete geometry -- General convexity -- Inequalities and extremum problems Partial differential equations -- Elliptic equations and systems -- Variational methods for second-order elliptic equations Convex and discrete geometry -- General convexity -- Convex sets in $n$ dimensions (including convex hypersurfaces) Partial differential equations -- Elliptic equations and systems -- Quasilinear elliptic equations with $p$-Laplacian |
| ISBN |
9781470470142
1470470144 |
| Classificazione | 35J6031B1539B6252A4035J2052A2035J92 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Notation and statement of results -- Basic estimates for A-harmonic functions -- Preliminary reductions for the proof of theorem A -- Proof of theorem A -- Final proof of theorem A -- Appendix -- Introduction and statement of results -- Boundary behavior of A-harmonic functions in Lipschitz domains -- Boundary Harnack inequalities -- Weak convergence of certain measures on Sn-1 -- The Hadamard variational formula for nonlinear capacity -- Proof of theorem B. |
| Record Nr. | UNINA-9910960758603321 |
Akman Murat
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| Providence : , : American Mathematical Society, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Local Lp-Brunn-Minkowski inequalities for p < 1 / / Alexander V. Kolesnikov, Emanuel Milman
| Local Lp-Brunn-Minkowski inequalities for p < 1 / / Alexander V. Kolesnikov, Emanuel Milman |
| Autore | Kolesnikov Alexander V |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 2022 |
| Descrizione fisica | 1 online resource (90 pages) |
| Disciplina |
516/.08
516.08 |
| Altri autori (Persone) | MilmanEmanuel |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Convex domains
Lp spaces Minkowski geometry Inequalities (Mathematics) Convex and discrete geometry -- General convexity -- Inequalities and extremum problems Convex and discrete geometry -- General convexity -- Asymptotic theory of convex bodies Partial differential equations -- Spectral theory and eigenvalue problems -- Estimation of eigenvalues, upper and lower bounds Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Spectral problems; spectral geometry; scattering theory |
| ISBN |
9781470470920
1470470926 |
| Classificazione | 52A4052A2335P1558J50 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title page -- Chapter 1. Introduction -- 1.1. Previously Known Partial Results -- 1.2. Main Results -- 1.3. Spectral Interpretation via the Hilbert-Brunn-Minkowski operator -- 1.4. Method of Proof -- 1.5. Applications -- Chapter 2. Notation -- Chapter 3. Global vs. Local Formulations of the ^{ }-Brunn-Minkowski Conjecture -- 3.1. Standard Equivalent Global Formulations -- 3.2. Global vs. Local ^{ }-Brunn-Minkowski -- Chapter 4. Local ^{ }-Brunn-Minkowski Conjecture -Infinitesimal Formulation -- 4.1. Mixed Surface Area and Volume of ² functions -- 4.2. Properties of Mixed Surface Area and Volume -- 4.3. Second ^{ }-Minkowski Inequality -- 4.4. Comparison with classical =1 case -- 4.5. Infinitesimal Formulation On ⁿ⁻¹ -- 4.6. Infinitesimal Formulation On ∂ -- Chapter 5. Relation to Hilbert-Brunn-Minkowski Operator and Linear Equivariance -- 5.1. Hilbert-Brunn-Minkowski operator -- 5.2. Linear equivariance of the Hilbert-Brunn-Minkowski operator -- 5.3. Spectral Minimization Problem and Potential Extremizers -- Chapter 6. Obtaining Estimates via the Reilly Formula -- 6.1. A sufficient condition for confirming the local -BM inequality -- 6.2. General Estimate on \D( ) -- 6.3. Examples -- Chapter 7. The second Steklov operator and \B( ₂ⁿ) -- 7.1. Second Steklov operator -- 7.2. Computing \B( ₂ⁿ) -- Chapter 8. Unconditional Convex Bodies and the Cube -- 8.1. Unconditional Convex Bodies -- 8.2. The Cube -- Chapter 9. Local log-Brunn-Minkowski via the Reilly Formula -- 9.1. Sufficient condition for verifying local log-Brunn-Minkowski -- 9.2. An alternative derivation via estimating \B( ) -- Chapter 10. Continuity of \B, \BNH, \D with application to _{ }ⁿ -- 10.1. Continuity of \B, \BNH, \D in -topology -- 10.2. The Cube -- 10.3. Unit-balls of ℓ_{ }ⁿ -- Chapter 11. Local Uniqueness for Even ^{ }-Minkowski Problem.
Chapter 12. Stability Estimates for Brunn-Minkowski and Isoperimetric Inequalities -- 12.1. New stability estimates for origin-symmetric convex bodies with respect to variance -- 12.2. Improved stability estimates for all convex bodies with respect to asymmetry -- Bibliography -- Back Cover. |
| Altri titoli varianti | Local |
| Record Nr. | UNINA-9910966324603321 |
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Kolesnikov Alexander V
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| Providence : , : American Mathematical Society, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Mathematics of shape description [[electronic resource] ] : a morphological approach to image processing and computer graphics / / Pijush K. Ghosh, Koichiro Deguchi
| Mathematics of shape description [[electronic resource] ] : a morphological approach to image processing and computer graphics / / Pijush K. Ghosh, Koichiro Deguchi |
| Autore | Ghosh Pijush K |
| Pubbl/distr/stampa | Singapore ; ; Hoboken, NJ, : Wiley, c2008 |
| Descrizione fisica | 1 online resource (272 p.) |
| Disciplina | 516.3/5 |
| Altri autori (Persone) | DeguchiKoichiro |
| Soggetto topico |
Geometry, Algebraic
Minkowski geometry Image processing - Mathematical models |
| ISBN |
1-282-03141-4
9786612031410 0-470-82309-7 0-470-82308-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
MATHEMATICS OF SHAPE DESCRIPTION; Contents; Foreword; Preface; 1 In Search of a Framework for Shape Description; 1.1 Shape Description: What It Means to Us; 1.2 Pure versus Pragmatic Approaches; 1.3 The In.uence of the Digital Computer on Our Approach to Shape Description; 1.4 A Metamodel for Shape Description; 1.4.1 A Mathematical Model for Shape Description and Associated Problems; 1.4.2 The Need for a Metamodel; 1.4.3 Reformulating the Metamodel to Adapt to the Pragmatic Approach; 1.5 The Metamodel within the Framework of Formal Language
1.5.1 An Introduction to Formal Languages and Grammars1.5.2 A Grammar for the Constructive Part of the Metamodel; 1.5.3 An Exploration of Shape Description Schemes in Terms of Formal Language Theory; 1.6 The Art of Model Making; 1.6.1 What is the Meaning of "Model"?; 1.6.2 A Few Guiding Principles; 1.7 Shape Description Schematics and the Tools of Mathematics; 1.7.1 Underlying Assumptions when Mapping from the Real World to a Mathematical System; 1.7.2 Fundamental Mathematical Structures and Their Various Compositions; 2 Sets and Functions for Shape Description; 2.1 Basic Concepts of Sets 2.1.1 De.nition of Sets2.1.2 Membership; 2.1.3 Speci.cations for a Set to Describe Shapes; 2.1.4 Special Sets; 2.2 Equality and Inclusion of Sets; 2.3 Some Operations on Sets; 2.3.1 The Power Set; 2.3.2 Set Union; 2.3.3 Set Intersection; 2.3.4 Set Difference; 2.3.5 Set Complement; 2.3.6 Symmetric Difference; 2.3.7 Venn Diagrams; 2.3.8 Cartesian Products; 2.4 Relations in Sets; 2.4.1 Fundamental Concepts; 2.4.2 The Properties of Binary Relations in a Set; 2.4.3 Equivalence Relations and Partitions; 2.4.4 Order Relations; 2.5 Functions, Mappings, and Operations; 2.5.1 Fundamental Concepts 2.5.2 The Graphical Representations of a Function2.5.3 The Range of a Function, and Various Categories of Function; 2.5.4 Composition of Functions; 2.5.5 The Inverse Function; 2.5.6 The One-to-One Onto Function and Set Isomorphism; 2.5.7 Equivalence Relations and Functions; 2.5.8 Functions of Many Variables, n-ary Operations; 2.5.9 A Special Type of Function: The Analytic Function; 3 Algebraic Structures for Shape Description; 3.1 What is an Algebraic Structure?; 3.1.1 Algebraic Systems with Internal Composition Laws; 3.1.2 Algebraic Systems with External Composition Laws 3.2 Properties of Algebraic Systems3.2.1 Associativity; 3.2.2 Commutativity; 3.2.3 Distributivity; 3.2.4 The Existence of the Identity/Unit Element; 3.2.5 The Existence of an Inverse Element; 3.3 Morphisms of Algebraic Systems; 3.4 Semigroups and Monoids: Two Simple Algebraic Systems; 3.5 Groups; 3.5.1 Fundamentals; 3.5.2 The Advantages of Identifying a System as a Group; 3.5.3 Transformation Groups; 3.6 Symmetry Groups; 3.6.1 The Action of a Group on a Set; 3.6.2 Translations and the Euclidean Group; 3.6.3 The Matrix Group; 3.7 Proper Rotations of Regular Solids 3.7.1 The Symmetry Groups of the Regular Solids |
| Record Nr. | UNINA-9910145959803321 |
|
Ghosh Pijush K
|
||
| Singapore ; ; Hoboken, NJ, : Wiley, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Mathematics of shape description : a morphological approach to image processing and computer graphics / / Pijush K. Ghosh, Koichiro Deguchi
| Mathematics of shape description : a morphological approach to image processing and computer graphics / / Pijush K. Ghosh, Koichiro Deguchi |
| Autore | Ghosh Pijush K |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore ; ; Hoboken, NJ, : Wiley, c2008 |
| Descrizione fisica | 1 online resource (272 p.) |
| Disciplina | 516.3/5 |
| Altri autori (Persone) | DeguchiKoichiro |
| Soggetto topico |
Geometry, Algebraic
Minkowski geometry Image processing - Mathematical models |
| ISBN |
9786612031410
9781282031418 1282031414 9780470823095 0470823097 9780470823088 0470823089 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
MATHEMATICS OF SHAPE DESCRIPTION; Contents; Foreword; Preface; 1 In Search of a Framework for Shape Description; 1.1 Shape Description: What It Means to Us; 1.2 Pure versus Pragmatic Approaches; 1.3 The In.uence of the Digital Computer on Our Approach to Shape Description; 1.4 A Metamodel for Shape Description; 1.4.1 A Mathematical Model for Shape Description and Associated Problems; 1.4.2 The Need for a Metamodel; 1.4.3 Reformulating the Metamodel to Adapt to the Pragmatic Approach; 1.5 The Metamodel within the Framework of Formal Language
1.5.1 An Introduction to Formal Languages and Grammars1.5.2 A Grammar for the Constructive Part of the Metamodel; 1.5.3 An Exploration of Shape Description Schemes in Terms of Formal Language Theory; 1.6 The Art of Model Making; 1.6.1 What is the Meaning of "Model"?; 1.6.2 A Few Guiding Principles; 1.7 Shape Description Schematics and the Tools of Mathematics; 1.7.1 Underlying Assumptions when Mapping from the Real World to a Mathematical System; 1.7.2 Fundamental Mathematical Structures and Their Various Compositions; 2 Sets and Functions for Shape Description; 2.1 Basic Concepts of Sets 2.1.1 De.nition of Sets2.1.2 Membership; 2.1.3 Speci.cations for a Set to Describe Shapes; 2.1.4 Special Sets; 2.2 Equality and Inclusion of Sets; 2.3 Some Operations on Sets; 2.3.1 The Power Set; 2.3.2 Set Union; 2.3.3 Set Intersection; 2.3.4 Set Difference; 2.3.5 Set Complement; 2.3.6 Symmetric Difference; 2.3.7 Venn Diagrams; 2.3.8 Cartesian Products; 2.4 Relations in Sets; 2.4.1 Fundamental Concepts; 2.4.2 The Properties of Binary Relations in a Set; 2.4.3 Equivalence Relations and Partitions; 2.4.4 Order Relations; 2.5 Functions, Mappings, and Operations; 2.5.1 Fundamental Concepts 2.5.2 The Graphical Representations of a Function2.5.3 The Range of a Function, and Various Categories of Function; 2.5.4 Composition of Functions; 2.5.5 The Inverse Function; 2.5.6 The One-to-One Onto Function and Set Isomorphism; 2.5.7 Equivalence Relations and Functions; 2.5.8 Functions of Many Variables, n-ary Operations; 2.5.9 A Special Type of Function: The Analytic Function; 3 Algebraic Structures for Shape Description; 3.1 What is an Algebraic Structure?; 3.1.1 Algebraic Systems with Internal Composition Laws; 3.1.2 Algebraic Systems with External Composition Laws 3.2 Properties of Algebraic Systems3.2.1 Associativity; 3.2.2 Commutativity; 3.2.3 Distributivity; 3.2.4 The Existence of the Identity/Unit Element; 3.2.5 The Existence of an Inverse Element; 3.3 Morphisms of Algebraic Systems; 3.4 Semigroups and Monoids: Two Simple Algebraic Systems; 3.5 Groups; 3.5.1 Fundamentals; 3.5.2 The Advantages of Identifying a System as a Group; 3.5.3 Transformation Groups; 3.6 Symmetry Groups; 3.6.1 The Action of a Group on a Set; 3.6.2 Translations and the Euclidean Group; 3.6.3 The Matrix Group; 3.7 Proper Rotations of Regular Solids 3.7.1 The Symmetry Groups of the Regular Solids |
| Record Nr. | UNINA-9910825787703321 |
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Ghosh Pijush K
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| Singapore ; ; Hoboken, NJ, : Wiley, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Minkowski geometry / A. C. Thompson
| Minkowski geometry / A. C. Thompson |
| Autore | Thompson, Anthony C. |
| Pubbl/distr/stampa | Cambridge ; New York : Cambridge University Press, 1996 |
| Descrizione fisica | xvi, 346 p. : ill. ; 24 cm |
| Disciplina | 516.374 |
| Collana | Encyclopedia of mathematics and its applications ; 63 |
| Soggetto topico | Minkowski geometry |
| ISBN | 052140472X |
| Classificazione |
AMS 51B20
LC QA685.T48 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001147549707536 |
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Thompson, Anthony C.
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| Cambridge ; New York : Cambridge University Press, 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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