Four lectures on scalar curvature
M Gromov - arxiv preprint arxiv:1908.10612, 2019 - arxiv.org
arxiv:1908.10612v6 [math.DG] 8 Jul 2021 Page 1 arxiv:1908.10612v6 [math.DG] 8 Jul 2021
Four Lectures on Scalar Curvature Misha Gromov July 9, 2021 Unlike manifolds with controlled …
Four Lectures on Scalar Curvature Misha Gromov July 9, 2021 Unlike manifolds with controlled …
Manifolds with density
F Morgan - Notices of the AMS, 2005 - ams.org
We consider a Riemannian manifold Mn with a positive density function Ψ (x) used to weight
volume and hypersurface area. In terms of the underlying Riemannian volume dV0 and area …
volume and hypersurface area. In terms of the underlying Riemannian volume dV0 and area …
On the role of convexity in isoperimetry, spectral gap and concentration
E Milman - Inventiones mathematicae, 2009 - Springer
We show that for convex domains in Euclidean space, Cheeger's isoperimetric inequality,
spectral gap of the Neumann Laplacian, exponential concentration of Lipschitz functions …
spectral gap of the Neumann Laplacian, exponential concentration of Lipschitz functions …
Minimising hulls, p-capacity and isoperimetric inequality on complete Riemannian manifolds
The notion of strictly outward minimising hull is investigated for open sets of finite perimeter
sitting inside a complete noncompact Riemannian manifold. Under natural geometric …
sitting inside a complete noncompact Riemannian manifold. Under natural geometric …
On the isoperimetric problem in Euclidean space with density
We study the isoperimetric problem for Euclidean space endowed with a continuous density.
In dimension one, we characterize isoperimetric regions for a unimodal density. In higher …
In dimension one, we characterize isoperimetric regions for a unimodal density. In higher …
On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth
In this paper we provide new existence results for isoperimetric sets of large volume in
Riemannian manifolds with nonnegative Ricci curvature and Euclidean volume growth. We …
Riemannian manifolds with nonnegative Ricci curvature and Euclidean volume growth. We …
Existence of hypersurfaces with prescribed mean curvature I-generic min-max
We prove that, for a generic set of smooth prescription functions $ h $ on a closed ambient
manifold, there always exists a nontrivial, smooth, closed hypersurface of prescribed mean …
manifold, there always exists a nontrivial, smooth, closed hypersurface of prescribed mean …
Isoperimetric sets in spaces with lower bounds on the Ricci curvature
In this paper we study regularity and topological properties of volume constrained
minimizers of quasi-perimeters in RCD spaces where the reference measure is the …
minimizers of quasi-perimeters in RCD spaces where the reference measure is the …
Deepcurrents: Learning implicit representations of shapes with boundaries
Recent techniques have been successful in reconstructing surfaces as level sets of learned
functions (such as signed distance fields) parameterized by deep neural networks. Many of …
functions (such as signed distance fields) parameterized by deep neural networks. Many of …
Min–max theory for constant mean curvature hypersurfaces
In this paper, we develop a min–max theory for the construction of constant mean curvature
(CMC) hypersurfaces of prescribed mean curvature in an arbitrary closed manifold. As a …
(CMC) hypersurfaces of prescribed mean curvature in an arbitrary closed manifold. As a …