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Global Riemannian Geometry: Curvature and Topology [[electronic resource] /] / by Ana Hurtado, Steen Markvorsen, Maung Min-Oo, Vicente Palmer
| Global Riemannian Geometry: Curvature and Topology [[electronic resource] /] / by Ana Hurtado, Steen Markvorsen, Maung Min-Oo, Vicente Palmer |
| Autore | Hurtado Ana |
| Edizione | [2nd ed. 2020.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2020 |
| Descrizione fisica | 1 online resource (VII, 121 p. 1 illus.) |
| Disciplina | 514.74 |
| Collana | Advanced Courses in Mathematics - CRM Barcelona |
| Soggetto topico |
Global analysis (Mathematics)
Manifolds (Mathematics) Differential geometry Complex manifolds Global Analysis and Analysis on Manifolds Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) |
| ISBN | 3-030-55293-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996418277703316 |
Hurtado Ana
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| Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Global Riemannian Geometry: Curvature and Topology / / by Ana Hurtado, Steen Markvorsen, Maung Min-Oo, Vicente Palmer
| Global Riemannian Geometry: Curvature and Topology / / by Ana Hurtado, Steen Markvorsen, Maung Min-Oo, Vicente Palmer |
| Autore | Hurtado Ana |
| Edizione | [2nd ed. 2020.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2020 |
| Descrizione fisica | 1 online resource (VII, 121 p. 1 illus.) |
| Disciplina | 514.74 |
| Collana | Advanced Courses in Mathematics - CRM Barcelona |
| Soggetto topico |
Global analysis (Mathematics)
Manifolds (Mathematics) Differential geometry Complex manifolds Global Analysis and Analysis on Manifolds Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) |
| ISBN | 3-030-55293-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910483915003321 |
|
Hurtado Ana
|
||
| Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
New Trends in Geometric Analysis : Spanish Network of Geometric Analysis 2007-2021 / / edited by Antonio Alarcón, Vicente Palmer, César Rosales
| New Trends in Geometric Analysis : Spanish Network of Geometric Analysis 2007-2021 / / edited by Antonio Alarcón, Vicente Palmer, César Rosales |
| Autore | Alarcón Antonio |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (398 pages) |
| Disciplina | 515.1 |
| Altri autori (Persone) |
PalmerVicente
RosalesCésar |
| Collana | RSME Springer Series |
| Soggetto topico |
Geometry
Mathematical analysis Analysis Geometria analítica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-39916-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Snapshots of Non-local Constrained Mean Curvature-Type Flows -- 1 Non-local Versus Unconstrained Mean Curvature Flow -- 1.1 The Classical Mean Curvature Flow -- 1.2 The Volume-Preserving Version of the Flow -- 2 The Area-Preserving Curve Shortening Flow -- 2.1 Evolution of Convex Curves -- 2.2 Basic Features for the Flow of Embedded Curves -- 2.3 Towards a Grayson-Type Theorem -- 2.4 Further Results -- 3 Volume-Preserving Mean Curvature-Type Flows -- 3.1 Convex Evolution and Stability Results -- 3.2 Free Boundary Problems with Rotational Symmetry -- 3.3 Evolution with Speeds Different from the Mean Curvature -- 3.4 Applications -- References -- Spherical Curves Whose Curvature Depends on Distanceto a Great Circle -- 1 Introduction -- 2 Spherical Curves such that κ= κ(z) and the Spherical Angular Momentum -- 3 Elastic-Type Curves on the Sphere -- 3.1 A New Characterization and a Generalization of Elastic Curves -- 3.2 Seiffert's Spherical Spirals -- 3.3 Borderline Spherical Elastic Curves -- 4 Loxodromic-Type Curves on the Sphere -- 4.1 Case 0 < -- μ< -- 1 : Spherical Loxodromes -- 4.2 Case μ=1 -- 4.3 Case μ> -- 1 -- 5 Spherical Catenaries -- 6 New and Classical Spherical Curves -- 6.1 Spherical Curves Such That κ(φ)=p cos2 φ/ cosφ, 0< -- p< -- 1 -- 6.2 Viviani's Curve and Spherical Archimedean Spirals -- References -- Conjugate Plateau Constructions in Product Spaces -- 1 Introduction -- 2 The Geometry of E(κ,τ)-spaces -- 2.1 Geodesics -- 2.2 Isometries -- 2.3 Working in Coordinates -- 2.3.1 A Global Model for Berger Spheres -- 2.3.2 The Half-Space Model -- 2.4 Fundamental Data -- 2.5 Cylinders and Multigraphs -- 3 The Conjugate Construction -- 3.1 Conjugate Curves -- 3.1.1 Vertical and Horizontal Geodesics -- 3.1.2 The Control of the Angle Function -- 3.1.3 Completion and Embeddedness.
3.2 Some Classes of Surfaces Preserved by the Sister Correspondence -- 3.2.1 Cylinders and Multigraphs -- 3.2.2 Surfaces with Zero Abresch-Rosenberg Differential -- 3.2.3 Ruled Minimal Surfaces -- 4 Dirichlet Problems for H-Surfaces in E(κ,τ) -- 4.1 The Plateau Problem -- 4.2 The Jenkins-Serrin Problem -- 5 Compact H-Surfaces in S2(κ)R -- 5.1 Horizontal Delaunay H-Surfaces -- 5.1.1 Construction of the Minimal Surface in M(4H2 + κ, H) -- 5.1.2 Analysis of the Angle Function -- 5.1.3 The Conjugate H-Immersion -- 5.1.4 Compactness -- 5.1.5 Embeddedness -- 5.2 Compact H-Surfaces of Arbitrary Genus in S2(κ)R -- 5.2.1 Regular Tessellations -- 5.2.2 Construction of the Minimal Surface in S3B(4H2+κ,H) -- 5.2.3 The Conjugate H-Immersion -- 5.2.4 Embeddedness -- 5.3 Compact Minimal Surfaces in S2(κ)S1(η) -- 5.3.1 Construction of the Minimal Surface in S2(κ)R -- 5.3.2 The Conjugate Minimal Surface -- 5.3.3 Compactness -- 6 Complete H-Surfaces in H2(κ)R -- 6.1 Genus Zero (H,k)-noids and (H,k)-nodoids in H2(κ)R -- 6.1.1 The Construction of the Minimal Surface in E(4H2+κ,H) -- 6.1.2 The Conjugate H-Immersion -- 6.1.3 Embeddedness -- 6.2 Genus One Minimal k-noids in H2(κ)R -- 6.2.1 The Minimal Surface in H2(κ)R -- 6.2.2 The Conjugate Minimal Surface -- 6.2.3 Solving the Period Problems -- 6.2.4 Embeddedness -- 7 Numerical Examples -- 7.1 Evolution to the Minimal Sphere -- 7.2 Singly Periodic Minimal Surfaces in S2 R -- 7.3 Final Remarks and Future Work -- References -- Integral Geometry of Pairs of Lines and Planes -- 1 Introduction -- 2 Preliminaries -- 2.1 Support Function -- 2.2 Measure of Lines in the Plane -- 2.3 Spherical Harmonics -- 3 Lower Bounds for the Hurwitz's Deficit -- 4 Integral Formulas for the Visual Angle -- 4.1 On Crofton and Hurwitz's Formulas -- 4.2 Measure of Pairs of Lines in the Plane -- 4.2.1 Crofton's Formula -- 4.2.2 Masotti's Formula. 4.2.3 Powers of Sine Formula -- 5 Integral Formulas for the Dihedral Angle -- 5.1 Invariant Measures in the Set of Ordered Pairs of Planes in the Space -- 5.2 Crofton's Formula in the Space -- References -- Homogeneous Hypersurfaces in Symmetric Spaces -- 1 Introduction -- 2 Homogeneous Hypersurfaces -- 2.1 Homogeneous Hypersurfaces and Cohomogeneity One Actions -- 2.2 Geometric Properties of Homogeneous Hypersurfaces -- 3 Symmetric Spaces -- 3.1 Definition and Fundamental Properties -- 3.2 Types of Symmetric Spaces -- 3.3 Symmetric Spaces of Noncompact Type: Root Space and Iwasawa Decompositions -- 3.4 Parabolic Subgroups and Subalgebras, and Boundary Components -- 4 Homogeneous Hypersurfaces in Compact Symmetric Spaces -- 4.1 Homogeneous Hypersurfaces of Round Spheres -- 4.2 Homogeneous Hypersurfaces in the Other Compact Symmetric Spaces -- 5 Homogeneous Hypersurfaces in Hyperbolic Spaces -- 5.1 Homogeneous Hypersurfaces in Real Hyperbolic Spaces -- 5.2 General Approach to Homogeneous Hypersurfaces in Hyperbolic Spaces -- 5.3 Homogeneous Hypersurfaces in Complex Hyperbolic Spaces -- 5.4 Homogeneous Hypersurfaces in Quaternionic Hyperbolic Spaces -- 5.5 Homogeneous Hypersurfaces in the Cayley Hyperbolic Plane -- 6 Homogeneous Hypersurfaces in Symmetric Spaces of Noncompact Type and Arbitrary Rank -- 6.1 Homogeneous Codimension One Foliations -- 6.2 Cohomogeneity One Actions with a Totally Geodesic Singular Orbit -- 6.3 Canonical Extension of Actions on Boundary Components -- 6.4 The Nilpotent Construction Method -- 6.5 The Classification of Cohomogeneity One Actions -- 7 Open Problems -- References -- First Dirichlet Eigenvalue and Exit Time Moments: A Survey -- 1 Introduction -- 2 Preliminaries: Poisson Hierarchy, Green Operator, Moment Spectrum, and Model Spaces -- 2.1 Poisson Hierarchy -- 2.2 Green Operator. 2.3 Radial Green Operator and Poisson Hierarchy for Geodesic Balls of Model Spaces -- 3 First Eigenvalue and Moment Spectrum -- 4 Comparison Results for the First Eigenvalue -- References -- Area-Minimizing Horizontal Graphs with Low Regularityin the Sub-Finsler Heisenberg Group H1 -- 1 Introduction -- 2 Preliminaries -- 2.1 The Heisenberg Group -- 2.2 Sub-Finsler Norms and Perimeter -- 3 The First Variation Formula and a Stationary Condition -- 4 Examples of Entire K-Perimeter-Minimizing Horizontal Graphs with One Singular Line -- 5 Area-Minimizing Cones in H1 -- References -- On the Double Soul Conjecture -- 1 Introduction -- 2 Context of Nonnegatively Curved Manifolds -- 3 Context of Double Disk Bundles -- 4 Difficulties for a Proof: Absence of Totally Geodesic Hypersurfaces and Souls -- 5 Construction of Examples as Double Disk Bundles -- 6 The Perfect Nonnegatively Curved Glued Metric and Some of Its Properties -- 7 Intertwining Results from Double Disk Bundles and Nonnegative Curvature -- 8 Proof for Biquotients -- 9 Relation to the Bott-Grove-Halperin Conjecture -- References -- Consequences and Extensions of the Brunn-Minkowski Theorem -- 1 Introduction -- 2 Deriving Grünbaum's Inequality as a Consequence of the Brunn-Minkowski Theorem -- 3 Discrete Brunn-Minkowski Type Inequalities for the Lattice Point Enumerator -- References -- An Account on Links Between Finsler and Lorentz Geometries for Riemannian Geometers -- 1 Introduction -- 2 A Motivating Example: Zermelo Navigation Problem -- 2.1 The Case of Mild Time-Independent Wind -- 2.1.1 Basic Finsler Setup -- 2.1.2 Classical Finslerian Solution to Zermelo Problem -- 2.1.3 Solution Using a Stationary Spacetime: Fermat Principle -- 2.2 The Case of Arbitrary Time-Independent Wind -- 2.2.1 Emergence of Wind Riemannian Structures -- 2.2.2 Solution Using an SSTK Spacetime. 2.3 The Time-Dependent Case -- 3 Relativistic Applications -- 3.1 Basic Lorentz Setup -- 3.2 The Initial Value Problem and Cauchy Hypersurfaces -- 3.3 Global Hyperbolicity and Causality of Spacetimes -- 3.4 Finsler Applications to Stationary Spacetimes -- 3.4.1 Background on the (Non-symmetric) Finslerian Distance dF -- 3.4.2 Finslerian Description of Causality -- 3.5 Application to General SSTK Spacetimes -- 3.5.1 The Particular Case ≥0 -- 3.5.2 The General Case -- 4 Finsler Applications -- 4.1 Randers-Kropina Metrics -- 4.2 Classification of Randers and Wind Riemannian Spaceforms -- 5 Interplay Finsler/Lorentz for Boundaries -- 5.1 Gromov Compactification for Incomplete Finslerian Manifolds -- 5.1.1 The Symmetric d Case -- 5.1.2 The Non-symmetric d Case -- 5.2 The Causal Boundary of a Spacetime -- 5.3 A New Busemann Boundary -- 5.4 The Causal Boundary of Stationary Spacetimes -- 5.4.1 The Static Case -- 5.4.2 The General Stationary Case -- 6 Lorentz-Finsler Metrics and Practical Applications -- 6.1 Anisotropic Wave Propagation and Huygens' Principle -- 6.2 Solution in Terms of Lorentz-Finsler Geodesics -- 6.3 Cut Points and Determination of the Wavefront -- 6.4 The Case of Wildfires -- References -- Geometric and Architectural Aspects of the Singular Minimal Surface Equation -- 1 Physical Motivation and the Variational Problem -- 2 Cylindrical Singular Minimal Surfaces -- 3 Singular Minimal Surfaces as Minimal Surfaces in a Conformal Space -- 4 Rotational Singular Minimal Surfaces -- 5 Comparison of Rotational Tectums with Catenary Rotation Surfaces and Paraboloids -- 6 Stability Results of Plateau-Rayleigh Type -- 7 Compact Singular Minimal Surfaces with Boundary -- References -- Geometry of [φ,e3]-Minimal Surfaces in R3 -- 1 Introduction -- 2 The Most Symmetric Examples -- 2.1 The One-dimensional Variational Problem. 2.2 Rotationally Symmetric Solutions. |
| Record Nr. | UNINA-9910754090703321 |
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Alarcón Antonio
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| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||