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Entropy and a convergence theorem for Gauss curvature flow in high dimension
- Source :
- Journal of the European Mathematical Society, vol 19, iss 12, JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, vol 19, iss 12
- Publication Year :
- 2017
- Publisher :
- eScholarship, University of California, 2017.
-
Abstract
- In this paper we prove uniform regularity estimates for the normalized Gauss curvature flow in higher dimensions. The convergence of solutions in $C^\infty$-topology to a smooth strictly convex soliton as $t$ approaches to infinity is obtained as a consequence of these estimates together with an earlier result of Andrews. The estimates are established via the study of a new entropy functional for the flow.
- Subjects :
- Mathematics - Differential Geometry
Gauss curvature flow
regularity
convergence
Applied Mathematics
General Mathematics
010102 general mathematics
Mathematical analysis
Regular polygon
support functions
01 natural sciences
Pure Mathematics
010101 applied mathematics
symbols.namesake
Differential Geometry (math.DG)
Gaussian curvature
symbols
FOS: Mathematics
Entropy (information theory)
0101 mathematics
Convex function
entropy
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Journal of the European Mathematical Society, vol 19, iss 12, JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, vol 19, iss 12
- Accession number :
- edsair.doi.dedup.....a170adb2eacd940815e70c6e6e385b88