Claudia Giesbert

Beomjun Choi (Pohang University, Korea): Liouville theorem for surfaces translating by sub-affine-critical powers of Gauss curvature

Wednesday, 15.06.2022 16:00 im Raum M5

Mathematik und Informatik

We classify the translators to the flows by sub-affine-critical powers of Gauss curvature. This corresponds to the classification of entire solutions to degenerate Monge-Ampere equation $\det D^2u = (1+|Du|^2)^{2-\frac{1}{2\alpha}}$ on $\mathbb{R}^2$ for $0<\alpha<1/4$. For the affine-critical-case $\det D^2u =1$, the classical result by Jorgens, Calabi and Pogorelov shows every solution must be a convex paraboloid and hence the level sets are homothetic ellipses. In our case, the level sets of given solution converge to a circle or a curve with $k$-fold symmetry for some $k>2$. These curves are closed shrinking curves to the $\frac {\alpha}{1-\alpha}$-curve shortening flow, classified by B. Andrews in 2003. This is a joint work with K. Choi and S. Kim.

Angelegt am Thursday, 10.02.2022 10:43 von Claudia Giesbert
Geändert am Tuesday, 31.05.2022 14:02 von Claudia Giesbert
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