7 papers
Sharp Neumann eigenvalue estimates and elliptic regularity in non-obtuse polyhedral domains
Nick Edelen, Chao Li
For integers , consider assertions: : Let be a spherical domain enclosed by totally geodesic 's with non-obtuse dihedral angles. The…
Entire area-minimizing surfaces in of density two are quadratic or planar
Nick Edelen, Luis Atzin Franco Reyna, Paul Minter
We classify any entire area-minimizing surface with density at infinity as either planar or algebraic, namely the zero set of a quadratic holomorphic p…
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…
Entire area-minimizing surfaces in R^4 are algebraic
Nick Edelen, Luis Atzin Franco Reyna, Paul Minter
We classify entire 2-dimensional area-minimizing or stable surfaces in R^4 with quadratic area growth as algebraic, cut out by a finite union of holomorphic polynomials whose colle…
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…