Nonexistence of isoperimetric sets in spaces of positive curvature

Variational inequalities (49J40) Global submanifolds (53C40) Global Riemannian geometry, including pinching (53C20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Cites Work

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Isoperimetric structure of asymptotically conical manifolds
Existence of isoperimetric regions in non-compact Riemannian manifolds under Ricci or scalar curvature conditions
Functions of bounded variation on ``good metric spaces
Manifolds of nonpositive curvature
On the connectivity of boundaries of sets minimizing perimeter subject to a volume constraint
The isoperimetric problem in complete surfaces of nonnegative curvature.
Large isoperimetric surfaces in initial data sets
Generalized existence of isoperimetric regions in non-compact Riemannian manifolds and applications to the isoperimetric profile
On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth
Isoperimetric sets in spaces with lower bounds on the Ricci curvature
Equivalent definitions of $BV$ space and of total variation on metric measure spaces
Rigidity of the 1-Bakry-Émery inequality and sets of finite Perimeter in RCD spaces
Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions
Effective versions of the positive mass theorem
Inner and outer smooth approximation of convex hypersurfaces. When is it possible?
Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature
A course in metric geometry
Isoperimetric regions in cones
Sets of finite perimeter and geometric variational problems. An introduction to geometric measure theory
Sur le volume minimal de ${R}\sp 2$
The Isoperimetric Inequality on Asymptotically Flat Manifolds with Nonnegative Scalar Curvature
Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones
Isoperimetric inequalities in unbounded convex bodies
The isoperimetric problemviadirect method in noncompact metric measure spaces with lower Ricci bounds
Isoperimetric Inequalities for Convex Cones
Alexandrov Geometry
Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds