70 citations · 514 across the 53 of their papers we have counts for
59 papers
Free boundary minimal surfaces of genus zero
Otis Chodosh, Matilde Gianocca
We prove that any embedded genus zero free boundary minimal surface in the ball has first Steklov eigenvalue . This implies the uniqueness of the critical catenoid.
Macroscopic scalar curvature bounds on surfaces
Otis Chodosh, Noa Vikman
We prove the generalized Geroch conjecture, and the corresponding hyperbolic conjecture, in dimension two.
No compromise in the liquid drop model
Otis Chodosh, Matilde Gianocca
We characterize minimizers in Gamow's liquid drop problem.
Minimal hypersurfaces of Morse index one
Otis Chodosh, Matilde Gianocca
We prove that a complete, connected, embedded, minimal hypersurface in with finite total curvature and Morse index one is the higher-dimensional catenoid.
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…
Minimal surfaces and comparison geometry
Otis Chodosh
We discuss applications of minimal surfaces to comparison geometry.
Generic regularity for minimizing hypersurfaces in dimension 11
Otis Chodosh, Christos Mantoulidis, Felix Schulze +1
We prove that area-minimizing hypersurfaces are generically smooth in ambient dimension in the context of the Plateau problem and of area minimization in integral homology. Fo…
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…
The p-widths of a polygon
Otis Chodosh, Sithipont Cholsaipant
The -widths are a nonlinear analogue of the spectrum of the Laplacian. We prove that each -width of a polygon in is achieved by a union of billiard trajectorie…
3-Manifolds with positive scalar curvature and bounded geometry
Otis Chodosh, Yi Lai, Kai Xu
We show that a complete contractible 3-manifold with positive scalar curvature and bounded geometry must be . We also show that an open handlebody of genus larger than…
Revisiting generic mean curvature flow in
Otis Chodosh, Kyeongsu Choi, Christos Mantoulidis +1
Bamler--Kleiner recently proved a multiplicity-one theorem for mean curvature flow in R^3 and combined it with the authors' work on generic mean curvature flows to fully resolve Hu…
Complete Riemannian 4-manifolds with uniformly positive scalar curvature
Otis Chodosh, Davi Maximo, Anubhav Mukherjee
We obtain topological obstructions to the existence of a complete Riemannian metric with uniformly positive scalar curvature on certain (non-compact) -manifolds. In particular,…
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…
On minimizers in the liquid drop model
Otis Chodosh, Ian Ruohoniemi
We prove that round balls of volume uniquely minimize in Gamow's liquid drop model.
Stable minimal hypersurfaces in
Otis Chodosh, Chao Li, Paul Minter +1
We show that a complete, two-sided, stable minimal hypersurface in is flat.
Mean Curvature Flow from Conical Singularities
Otis Chodosh, J. M. Daniels-Holgate, Felix Schulze
We prove Ilmanen's resolution of point singularities conjecture by establishing short-time smoothness of the level set flow of a smooth hypersurface with isolated conical singulari…
Mean curvature flow with generic low-entropy initial data II
Otis Chodosh, Christos Mantoulidis, Felix Schulze
We prove that the mean curvature flow of a generic closed embedded hypersurface in or with entropy , or with entropy if…
Improved generic regularity of codimension-1 minimizing integral currents
Otis Chodosh, Christos Mantoulidis, Felix Schulze
Let be a smooth, closed, oriented, -dimensional submanifold of . We show that there exist arbitrarily small perturbations of with the property…
On the Minkowski inequality near the sphere
Otis Chodosh, Michael Eichmair, Thomas Koerber
We construct a sequence of closed, axially symmetric surfaces that converges to the unit sphere in for e…
Mean curvature flow with generic initial data II
Otis Chodosh, Kyeongsu Choi, Felix Schulze
We show that the mean curvature flow of a generic closed surface in avoids multiplicity one tangent flows that are not round spheres/cylinders. In particular, we sho…
Generic regularity for minimizing hypersurfaces in dimensions 9 and 10
Otis Chodosh, Christos Mantoulidis, Felix Schulze
We prove that singularities of area minimizing hypersurfaces can be perturbed away in ambient dimensions 9 and 10.
Volume growth of 3-manifolds with scalar curvature lower bounds
Otis Chodosh, Chao Li, Douglas Stryker
We give a new proof of a recent result of Munteanu--Wang relating scalar curvature to volume growth on a -manifold with non-negative Ricci curvature. Our proof relies on the the…
Stable anisotropic minimal hypersurfaces in
Otis Chodosh, Chao Li
We show that a complete, two-sided, stable immersed anisotropic minimal hypersurface in has intrinsic cubic volume growth, provided the parametric elliptic integral…
Complete stable minimal hypersurfaces in positively curved 4-manifolds
Otis Chodosh, Chao Li, Douglas Stryker
We show that the combination of non-negative sectional curvature (or -intermediate Ricci curvature) and strict positivity of scalar curvature forces rigidity of complete (non-co…