Entropy and a convergence theorem for Gauss curvature flow in high dimension
By Pengfei Guan, Lei Ni. 2013
102 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Astronomy and Astrophysics
View Paper: https://www.semanticscholar.org/paper/e1381a029299d423cc30f4c0401d4ea41094908b
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In Applied Mathematics
In Astronomy and Astrophysics
Citations in the corpus
- Asymptotic behavior of flows by powers of the Gaussian curvature (2016, unknown): “This was proved by Andrews [3] for α∈[1/(n+2), 1/n]; by Guan and Ni [16] for α=1; and by Andrews, Guan, and Ni [5] for all α∈(1/(n+2),∞).”
- A flow method for the dual Orlicz–Minkowski problem (2020, unknown): “[2, 3, 9, 10, 13, 16, 19, 24, 25, 37, 61, 62] and references therein.”
- Variations of a class of Monge–Ampère-type functionals and their applications (2021, background): “When p = 0 and q = n + 1, the second variation of the functional was obtained in [22].”