An excursion into geometric analysis. (English) Zbl 1076.53001
Grigor’yan, Alexander (ed.) et al., Surveys in differential geometry. Eigenvalues of Laplacians and other geometric operators. Somerville, MA: International Press (ISBN 1-57146-115-9/hbk). Surveys in Differential Geometry 9, 83-146 (2004).
Guided by the theory of minimal surfaces, the authors survey a number of basic results in geometric analysis. Monotonicity formulas, gradient estimates, regularity theory, growth of harmonic functions are just a few of the topics approached. For a complete listing, see the table of contents. The paper is definitely an interesting presentation of some key elements originating in the study of minimal surfaces, but later used and extended for other purposes: curvature flows, function theory of manifolds with non-negative Ricci curvature. A number of open questions which arise naturally is also presented.
For the entire collection see [Zbl 1050.53002].
For the entire collection see [Zbl 1050.53002].
Reviewer: Alina Stancu (Lowell)
MSC:
| 53-02 | Research exposition (monographs, survey articles) pertaining to differential geometry |
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
| 53C23 | Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces |
| 53C43 | Differential geometric aspects of harmonic maps |
