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Geometric analysis /

Li, Peter, (1952-)

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Geometric analysis /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Geometric analysis // Peter Li.
作者:	Li, Peter,
出版者:	Cambridge :Cambridge University Press, : 2012.,
面頁冊數:	x, 406 p. :ill ;24 cm.
標題:	Geometric analysis. -
電子資源:	http://assets.cambridge.org/97811070/20641/cover/9781107020641.jpg
ISBN:	9781107020641 (hbk.) :

Geometric analysis /
Li, Peter,1952-

Geometric analysis /Peter Li. - Cambridge :Cambridge University Press,2012. - x, 406 p. :ill ;24 cm. - Cambridge studies in advanced mathematics ;134.

Includes bibliographical references (p. 399-403) and index.

First and second variational formulas for area --

"The aim of this graduate-level text is to equip the reader with the basic tools and techniques needed for research in various areas of geometric analysis. Throughout, the main theme is to present the interaction of partial differential equations and differential geometry. More specifically, emphasis is placed on how the behavior of the solutions of a PDE is affected by the geometry of the underlying manifold and vice versa. For efficiency the author mainly restricts himself to the linear theory and only a rudimentary background in Riemannian geometry and partial differential equations is assumed. Originating from the author’s own lectures, this book is an ideal introduction for graduate students, as well as a useful reference for experts in the field"--

ISBN: 9781107020641 (hbk.) :US75.00

LCCN: 2011051365Subjects--Topical Terms:

1439441
Geometric analysis.

LC Class. No.: QA360 / .L53 2012

Dewey Class. No.: 515/.1

Geometric analysis /
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245 1 0 $a Geometric analysis / $c Peter Li.
260 # $a Cambridge : $b Cambridge University Press, $c 2012.
300 $a x, 406 p. : $b ill ; $c 24 cm.
490 1 0 $a Cambridge studies in advanced mathematics ; $v 134
504 $a Includes bibliographical references (p. 399-403) and index.
505 $t First and second variational formulas for area -- $t Volume comparison theorem -- $t Bochner-Weitzenböck formulas -- $t Laplacian comparison theorem -- $t Poincare inequality and the first eigenvalue -- $t Gradient estimate and Harnack inequality -- $t Mean value inequality -- $t Reilly's formula and applications -- $t Isoperimetric inequalities and Sobolev inequalities -- $t The heat equation -- $t Properties and estimates of the heat kernel -- $t Gradient estimate and Harnack inequality for the heat equation -- $t Upper and lower bounds for the heat kernel -- $t Sobolev inequality, Poincare inequality and parabolic mean value inequality -- $t Uniqueness and maximum principle for the heat equation -- $t Large time behavior of the heat kernel -- $t Green's function -- $t Measured Neumann-Poincare inequality and measured Sobolev inequality -- $t Parabolic Harnack inequality and regularity theory -- $t Parabolicity -- $t Harmonic functions and ends -- $t Manifolds with positive spectrum -- $t Manifolds with Ricci curvature bounded from below -- $t Manifolds with finite volume -- $t Stability of minimal hypersurfaces in a 3-manifold -- $t Stability of minimal hypersurfaces in a higher dimensional manifold -- $t Linear growth harmonic functions -- $t Polynomial growth harmonic functions -- $t Lq harmonic functions -- $t Mean value constant, Liouville property, and minimal submanifolds -- $t Massive sets -- $t The structure of harmonic maps into a Cartan-Hadamard manifold -- $t Appendix A : Computation of warped product metrics -- $t Appendix B : Polynomial growth harmonic functions on Euclidean space; References.
520 # $a "The aim of this graduate-level text is to equip the reader with the basic tools and techniques needed for research in various areas of geometric analysis. Throughout, the main theme is to present the interaction of partial differential equations and differential geometry. More specifically, emphasis is placed on how the behavior of the solutions of a PDE is affected by the geometry of the underlying manifold and vice versa. For efficiency the author mainly restricts himself to the linear theory and only a rudimentary background in Riemannian geometry and partial differential equations is assumed. Originating from the author’s own lectures, this book is an ideal introduction for graduate students, as well as a useful reference for experts in the field"-- $c Provided by publisher.
650 # 0 $a Geometric analysis. $3 1439441
856 4 2 $3 Cover image $u http://assets.cambridge.org/97811070/20641/cover/9781107020641.jpg