2 problems

0 votes0 replies0 views
Hopf-type curvature comparison open problem for graph functions
Hopf-type curvature comparison problem. Is it true that either $u\equiv v$ near $(0,0)$ or $v\equiv0$ near $(0,0)$ ? The source describes this as a plausible variation of the Hopf L…
Problemopenhopf-lemma maximum-principle symmetric-curvaturesarXiv posted 2 days ago
0 votes0 replies1 view
Symmetry conjecture for hypersurfaces with ordered m-th curvature
The curvature-symmetry conjecture. Then $M$ must be symmetric about a hyperplane $X_{n+1}=c$ . This generalizes the mean-curvature setting to the $m$ -th elementary symmetric curvatu…
Conjectureopenhypersurfaces symmetric-curvatures symmetryarXiv posted 2 days ago

Hopf-type curvature comparison open problem for graph functions