70 citations · 254 across the 21 of their papers we have counts for
22 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…
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…
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.
Double-well phase transitions are more rigid than minimal hypersurfaces
Christos Mantoulidis
In this short note we see that double-well phase transitions exhibit more rigidity than their minimal hypersurface counterparts.
Decomposing 4-manifolds with positive scalar curvature
Richard H. Bamler, Chao Li, Christos Mantoulidis
We show that every closed, oriented, topologically PSC 4-manifold can be obtained via 0 and 1-surgeries from a topologically PSC 4-orbifold with vanishing first Betti number and se…
The p-widths of a surface
Otis Chodosh, Christos Mantoulidis
The -widths of a closed Riemannian manifold are a nonlinear analogue of the spectrum of its Laplace--Beltrami operator, which corresponds to areas of a certain min-max sequence…
Metrics with and flexibility in the Riemannian Penrose Inequality
Chao Li, Christos Mantoulidis
On a closed manifold, consider the space of all Riemannian metrics for which -Delta + kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectra…
Mean curvature flow with generic low-entropy initial data
Otis Chodosh, Kyeongsu Choi, Christos Mantoulidis +1
We prove that sufficiently low-entropy closed hypersurfaces can be perturbed so that their mean curvature flow encounters only spherical and cylindrical singularities. Our theorem…
Variational aspects of phase transitions with prescribed mean curvature
Christos Mantoulidis
We study the spectrum of phase transitions with prescribed mean curvature in Riemannian manifolds. These phase transitions are solutions to an inhomogeneous semilinear elliptic PDE…
Mean curvature flow with generic initial data
Otis Chodosh, Kyeongsu Choi, Christos Mantoulidis +1
We show that the mean curvature flow of generic closed surfaces in avoids asymptotically conical and non-spherical compact singularities. We also show that the mea…
Ancient gradient flows of elliptic functionals and Morse index
Kyeongsu Choi, Christos Mantoulidis
We study closed ancient solutions to gradient flows of elliptic functionals in Riemannian manifolds, including mean curvature flow and harmonic map heat flow. Our work has various…
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…
Minimal surfaces and the Allen-Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates
Otis Chodosh, Christos Mantoulidis
The Allen-Cahn equation is a semilinear PDE which is deeply linked to the theory of minimal hypersurfaces via a singular limit. We prove curvature estimates and strong sheet separa…
Positive scalar curvature with skeleton singularities
Chao Li, Christos Mantoulidis
We study positive scalar curvature on the regular part of Riemannian manifolds with singular, uniformly Euclidean () metrics that consolidate Gromov's scalar curvature po…
Allen-Cahn min-max on surfaces
Christos Mantoulidis
We use a min-max procedure on the Allen-Cahn energy functional to construct geodesics on closed, 2-dimensional Riemannian manifolds, as motivated by the work of Guaraco. Borrowing…
A note on the Morse index of 2k-ended phase transitions in R^2
Christos Mantoulidis
We show that the Morse index of every 2k-ended solution of the Allen-Cahn equation in R^2 is >= k-1. This bound is expected to be sharp.
Total mean curvature, scalar curvature, and a variational analog of Brown-York mass
Christos Mantoulidis, Pengzi Miao
We study the supremum of the total mean curvature on the boundary of compact, mean-convex 3-manifolds with nonnegative scalar curvature, and a prescribed boundary metric. We establ…
On the Bartnik mass of apparent horizons
Christos Mantoulidis, Richard Schoen
In this paper we characterize the intrinsic geometry of apparent horizons (outermost marginally outer trapped surfaces) in asymptotically flat spacetimes; that is, the Riemannian m…