Liouville Theorem for Surfaces Translating by Sub-Affine-Critical Powers of Gauss Curvature
Time: 2022-06-08
Published By: Wenqiong Li
Speaker(s): Beomjun Choi (Pohang University of Science and Technology)
Time: 09:00-10:00 June 15, 2022
Venue: Online
Abstract:
Speaker: Beomjun Choi
PhD at Columbia University, 2019.05
Research area: geometric analysis and partial differential equations
Zoom:
Link: https://us02web.zoom.us/j/83934273174?pwd=bGk1cFk1NmFXbHNOV25XYy9CVlVQdz09
ID: 839 3427 3174
Password: 324536
We classify the translators to the flows by sub-affine-critical powers of Gauss curvature in $\mathbb{R}^3$. If $\alpha$ denotes the power, this is a Liouville theorem for degenerate Monge-Ampere equations $\det D^2u = (1+|Du|^2)^{2-\frac{1}{2\alpha}}$ for $0<\alpha<1/4$. For the affine-critical-case $\det D^2u =1$, the classical result by Jorgens, Calabi and Pogorelov shows the level curves of given solution are homothetic ellipses. In our case, the level curves converge asymptotically to a round circle or a curve with $k$-fold symmetry for some $k>2$. More precisely, these curves are closed shrinking curves to the $\frac {\alpha}{1-\alpha}$-curve shortening flow that were previously classified by B. Andrews in 2003. This is a joint work with K. Choi and S. Kim.
Speaker: Beomjun Choi
Assistant Professor at POSTECH, Republic of Korea, 2021.07 ~
CMC Fellow at KIAS, Republic of Korea, 2021.05 ~ 2021.06
Postdoc at University of Toronto, 2019.08 ~ 2021.04
PhD at Columbia University, 2019.05
Research area: geometric analysis and partial differential equations
Zoom:
Link: https://us02web.zoom.us/j/83934273174?pwd=bGk1cFk1NmFXbHNOV25XYy9CVlVQdz09
ID: 839 3427 3174
Password: 324536
