Geodesic
Entropy and a convergence theorem for Gauss curvature flow in high dimension
Journal of the European Mathematical Society, Tome 19 (2017) no. 12, pp. 3735-3761

Voir la notice de l'article provenant de la source EMS Press

We prove uniform regularity estimates for the normalized Gauss curvature flow in higher dimensions. The convergence of solutions in C∞-topology to a smooth strictly convex soliton as t goes 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 an entropy functional for convex bodies.
DOI : 10.4171/jems/752
Classification : 35-XX, 53-XX, 58-XX
Keywords: Gauss curvature flow, entropy, support functions, regularity, convergence 
@article{JEMS_2017_19_12_a5,
     author = {Pengfei Guan and Lei Ni},
     title = {Entropy and a convergence theorem for {Gauss} curvature flow in high dimension},
     journal = {Journal of the European Mathematical Society},
     pages = {3735--3761},
     publisher = {mathdoc},
     volume = {19},
     number = {12},
     year = {2017},
     doi = {10.4171/jems/752},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/752/}
}
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Pengfei Guan; Lei Ni. Entropy and a convergence theorem for Gauss curvature flow in high dimension. Journal of the European Mathematical Society, Tome 19 (2017) no. 12, pp. 3735-3761. doi: 10.4171/jems/752

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