7 papers
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…
Almgren's Three-Legged Starfish
Christos Mantoulidis, Jared Marx-Kuo
In this note we use classical tools from min-max and hyperbolic geometry to substantiate a folklore example in Almgren--Pitts min-max theory, the three-legged starfish metric on a…
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…
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…
Minimal hypersurfaces with arbitrarily large area
Otis Chodosh, Christos Mantoulidis
For 3 n 7, we prove that a bumpy closed Riemannian n-manifold contains a sequence of connected embedded closed minimal surfaces with unbounded area.
Capacity, quasi-local mass, and singular fill-ins
Christos Mantoulidis, Pengzi Miao, Luen-Fai Tam
We derive new inequalities between the boundary capacity of an asymptotically flat 3-manifold with nonnegative scalar curvature and boundary quantities that relate to quasi-local m…