5 papers
A Bernstein-type theorem for capillary graphs in a half-space
Nick Edelen, Chao Li, Jonathan J. Zhu
We show that any entire, capillary minimal graph in a half-space must be linear in low-dimensions or, more generally, when some tangent cone at infinity does not split off a vertic…
Immersions with small normal curvature
Otis Chodosh, Chao Li
We study Gromov's problem concerning minimal normal curvature immersions in the unit ball. In particular, we determine the minimal possible value of the normal curvature of an $S^n…
Stable minimal hypersurfaces in
Otis Chodosh, Chao Li, Paul Minter +1
We show that a complete, two-sided, stable minimal hypersurface in is flat.
Weiss monotonicity and capillary hypersurfaces
Otis Chodosh, Nick Edelen, Chao Li
Previous work of the authors established the rigorous limiting behavior of minimizing capillary surfaces to minimizers of the Alt--Caffarelli functional as the capillary angle tend…
Improved regularity for minimizing capillary hypersurfaces
Otis Chodosh, Nick Edelen, Chao Li
We give improved estimates for the size of the singular set of minimizing capillary hypersurfaces: the singular set is always of codimension at least , and this estimate improve…