7 papers
The Riemannian Quantitative Isoperimetric Inequality
Otis Chodosh, Max Engelstein, Luca Spolaor
We study the Riemannian quantiative isoperimetric inequality. We show that direct analogue of the Euclidean quantitative isoperimetric inequality is--in general--false on a closed…
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.
On the topology and index of minimal surfaces II
Otis Chodosh, Davi Maximo
For an immersed minimal surface in , we show that there exists a lower bound on its Morse index that depends on the genus and number of ends, counting multiplicity. T…
A splitting theorem for scalar curvature
Otis Chodosh, Michael Eichmair, Vlad Moraru
We show that a Riemannian -manifold with non-negative scalar curvature is flat if it contains an area-minimizing cylinder. This scalar-curvature analogue of the classical splitt…
Characterization of large isoperimetric regions in asymptotically hyperbolic initial data
Otis Chodosh, Michael Eichmair, Yuguang Shi +1
Let be a complete Riemannian -manifold asymptotic to Schwarzschild-anti-deSitter and with scalar curvature . Building on work of A.~Neves and G.~Tian and of…
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…