8 papers · 1 filter
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…
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…