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The analysis of harmonic maps and their heat flows [[electronic resource] /] / Fanghua Lin, Changyou Wang
| The analysis of harmonic maps and their heat flows [[electronic resource] /] / Fanghua Lin, Changyou Wang |
| Autore | Lin Fanghua |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2008 |
| Descrizione fisica | 1 online resource (280 p.) |
| Disciplina | 514/.74 |
| Altri autori (Persone) | WangChangyou <1967-> |
| Soggetto topico |
Harmonic maps
Heat equation Riemannian manifolds |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-93808-4
9786611938086 981-277-953-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; 3.2 Weakly harmonic maps in dimension two; 3.3 Stationary harmonic maps in higher dimensions; Preface; Organization of the book; Acknowledgements; 1 Introduction to harmonic maps; 1.1 Dirichlet principle of harmonic maps; 1.2 Intrinsic view of harmonic maps; 1.3 Extrinsic view of harmonic maps; 1.4 A few facts about harmonic maps; 1.5 Bochner identity for harmonic maps; 1.6 Second variational formula of harmonic maps; 2 Regularity of minimizing harmonic maps; 2.1 Minimizing harmonic maps in dimension two; 2.2 Minimizing harmonic maps in higher dimensions
2.3 Federer's dimension reduction principle2.4 Boundary regularity for minimizing harmonic maps; 2.5 Uniqueness of minimizing tangent maps; 2.6 Integrability of Jacobi fields and its applications; 3 Regularity of stationary harmonic maps; 3.1 Weakly harmonic maps into regular balls; 3.4 Stable-stationary harmonic maps into spheres; 4 Blow up analysis of stationary harmonic maps; 4.1 Preliminary analysis; 4.2 Rectifiability of defect measures; 4.3 Strong convergence and interior gradient estimates; 4.4 Boundary gradient estimates; 5 Heat ows to Riemannian manifolds of NPC; 5.1 Motivation 5.2 Existence of short time smooth solutions5.3 Existence of global smooth solutions under RN < 0; 5.4 An extension of Eells-Sampson's theorem; 6 Bubbling analysis in dimension two; 6.1 Minimal immersion of spheres; 6.2 Almost smooth heat ows in dimension two; 6.3 Finite time singularity in dimension two; 6.4 Bubbling phenomena for 2-D heat ows; 6.5 Approximate harmonic maps in dimension two; 7 Partially smooth heat ows; 7.1 Monotonicity formula and a priori estimates; 7.2 Global smooth solutions and weak compactness; 7.3 Finite time singularity in dimensions at least three 7.4 Nonuniqueness of heat flow of harmonic maps7.5 Global weak heat flows into spheres; 7.6 Global weak heat flows into general manifolds; 8 Blow up analysis on heat ows; 8.1 Obstruction to strong convergence; 8.2 Basic estimates; 8.3 Stratification of the concentration set; 8.4 Blow up analysis in dimension two; 8.5 Blow up analysis in dimensions n > 3; 9 Dynamics of defect measures in heat flows; 9.1 Generalized varifolds and rectifiability; 9.2 Generalized varifold flows and Brakke's motion; 9.3 Energy quantization of the defect measure; 9.4 Further remarks; Bibliography; Index |
| Record Nr. | UNINA-9910454064403321 |
Lin Fanghua
|
||
| Hackensack, NJ, : World Scientific, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The analysis of harmonic maps and their heat flows [[electronic resource] /] / Fanghua Lin, Changyou Wang
| The analysis of harmonic maps and their heat flows [[electronic resource] /] / Fanghua Lin, Changyou Wang |
| Autore | Lin Fanghua |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2008 |
| Descrizione fisica | 1 online resource (280 p.) |
| Disciplina | 514/.74 |
| Altri autori (Persone) | WangChangyou <1967-> |
| Soggetto topico |
Harmonic maps
Heat equation Riemannian manifolds |
| ISBN |
1-281-93808-4
9786611938086 981-277-953-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; 3.2 Weakly harmonic maps in dimension two; 3.3 Stationary harmonic maps in higher dimensions; Preface; Organization of the book; Acknowledgements; 1 Introduction to harmonic maps; 1.1 Dirichlet principle of harmonic maps; 1.2 Intrinsic view of harmonic maps; 1.3 Extrinsic view of harmonic maps; 1.4 A few facts about harmonic maps; 1.5 Bochner identity for harmonic maps; 1.6 Second variational formula of harmonic maps; 2 Regularity of minimizing harmonic maps; 2.1 Minimizing harmonic maps in dimension two; 2.2 Minimizing harmonic maps in higher dimensions
2.3 Federer's dimension reduction principle2.4 Boundary regularity for minimizing harmonic maps; 2.5 Uniqueness of minimizing tangent maps; 2.6 Integrability of Jacobi fields and its applications; 3 Regularity of stationary harmonic maps; 3.1 Weakly harmonic maps into regular balls; 3.4 Stable-stationary harmonic maps into spheres; 4 Blow up analysis of stationary harmonic maps; 4.1 Preliminary analysis; 4.2 Rectifiability of defect measures; 4.3 Strong convergence and interior gradient estimates; 4.4 Boundary gradient estimates; 5 Heat ows to Riemannian manifolds of NPC; 5.1 Motivation 5.2 Existence of short time smooth solutions5.3 Existence of global smooth solutions under RN < 0; 5.4 An extension of Eells-Sampson's theorem; 6 Bubbling analysis in dimension two; 6.1 Minimal immersion of spheres; 6.2 Almost smooth heat ows in dimension two; 6.3 Finite time singularity in dimension two; 6.4 Bubbling phenomena for 2-D heat ows; 6.5 Approximate harmonic maps in dimension two; 7 Partially smooth heat ows; 7.1 Monotonicity formula and a priori estimates; 7.2 Global smooth solutions and weak compactness; 7.3 Finite time singularity in dimensions at least three 7.4 Nonuniqueness of heat flow of harmonic maps7.5 Global weak heat flows into spheres; 7.6 Global weak heat flows into general manifolds; 8 Blow up analysis on heat ows; 8.1 Obstruction to strong convergence; 8.2 Basic estimates; 8.3 Stratification of the concentration set; 8.4 Blow up analysis in dimension two; 8.5 Blow up analysis in dimensions n > 3; 9 Dynamics of defect measures in heat flows; 9.1 Generalized varifolds and rectifiability; 9.2 Generalized varifold flows and Brakke's motion; 9.3 Energy quantization of the defect measure; 9.4 Further remarks; Bibliography; Index |
| Record Nr. | UNINA-9910782558103321 |
|
Lin Fanghua
|
||
| Hackensack, NJ, : World Scientific, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The analysis of harmonic maps and their heat flows / / Fanghua Lin, Changyou Wang
| The analysis of harmonic maps and their heat flows / / Fanghua Lin, Changyou Wang |
| Autore | Lin Fanghua |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2008 |
| Descrizione fisica | 1 online resource (280 p.) |
| Disciplina | 514/.74 |
| Altri autori (Persone) | WangChangyou <1967-> |
| Soggetto topico |
Harmonic maps
Heat equation Riemannian manifolds |
| ISBN |
1-281-93808-4
9786611938086 981-277-953-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; 3.2 Weakly harmonic maps in dimension two; 3.3 Stationary harmonic maps in higher dimensions; Preface; Organization of the book; Acknowledgements; 1 Introduction to harmonic maps; 1.1 Dirichlet principle of harmonic maps; 1.2 Intrinsic view of harmonic maps; 1.3 Extrinsic view of harmonic maps; 1.4 A few facts about harmonic maps; 1.5 Bochner identity for harmonic maps; 1.6 Second variational formula of harmonic maps; 2 Regularity of minimizing harmonic maps; 2.1 Minimizing harmonic maps in dimension two; 2.2 Minimizing harmonic maps in higher dimensions
2.3 Federer's dimension reduction principle2.4 Boundary regularity for minimizing harmonic maps; 2.5 Uniqueness of minimizing tangent maps; 2.6 Integrability of Jacobi fields and its applications; 3 Regularity of stationary harmonic maps; 3.1 Weakly harmonic maps into regular balls; 3.4 Stable-stationary harmonic maps into spheres; 4 Blow up analysis of stationary harmonic maps; 4.1 Preliminary analysis; 4.2 Rectifiability of defect measures; 4.3 Strong convergence and interior gradient estimates; 4.4 Boundary gradient estimates; 5 Heat ows to Riemannian manifolds of NPC; 5.1 Motivation 5.2 Existence of short time smooth solutions5.3 Existence of global smooth solutions under RN < 0; 5.4 An extension of Eells-Sampson's theorem; 6 Bubbling analysis in dimension two; 6.1 Minimal immersion of spheres; 6.2 Almost smooth heat ows in dimension two; 6.3 Finite time singularity in dimension two; 6.4 Bubbling phenomena for 2-D heat ows; 6.5 Approximate harmonic maps in dimension two; 7 Partially smooth heat ows; 7.1 Monotonicity formula and a priori estimates; 7.2 Global smooth solutions and weak compactness; 7.3 Finite time singularity in dimensions at least three 7.4 Nonuniqueness of heat flow of harmonic maps7.5 Global weak heat flows into spheres; 7.6 Global weak heat flows into general manifolds; 8 Blow up analysis on heat ows; 8.1 Obstruction to strong convergence; 8.2 Basic estimates; 8.3 Stratification of the concentration set; 8.4 Blow up analysis in dimension two; 8.5 Blow up analysis in dimensions n > 3; 9 Dynamics of defect measures in heat flows; 9.1 Generalized varifolds and rectifiability; 9.2 Generalized varifold flows and Brakke's motion; 9.3 Energy quantization of the defect measure; 9.4 Further remarks; Bibliography; Index |
| Record Nr. | UNINA-9910814555403321 |
|
Lin Fanghua
|
||
| Hackensack, NJ, : World Scientific, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||