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The isoperimetric profile of a smooth Riemannian manifold for small volumes
We define a new class of submanifolds called pseudo-bubbles, defined by an equation weaker than constancy of mean curvature. We show that in a neighborhood of each point of a Riemannian manifold,…
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A discontinuous isoperimetric profile for a complete Riemannian manifold
The first known example of a complete Riemannian manifold whose isoperimetric profile is discontinuous is given.
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Generalized existence of isoperimetric regions in non-compact Riemannian manifolds and applications to the isoperimetric profile
For a complete noncompact connected Riemannian manifold with bounded geometry, we prove the existence of isoperimetric regions in a larger space obtained by adding finitely many limit manifolds at…
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Existence of isoperimetric regions in non-compact Riemannian manifolds under Ricci or scalar curvature conditions
We prove existence of isoperimetric regions for every volume in non-compact Riemannian $n$-manifolds $(M,g)$, $n\geq 2$, having Ricci curvature $Ric_g\geq (n-1) k_0 g$ and being locally asymptotic to…
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Continuity and differentiability properties of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry
For a complete noncompact connected Riemannian manifold with bounded geometry $M^n$, we prove that the isoperimetric profile function $I_{M^n}$ is continuous. Here for bounded geometry we mean that…
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Regularity of Isoperimetric Regions that are Close to a Smooth Manifold
In this paper we prove a regularity theorem for isoperimetric regions T that are close in flat norm to an open bounded set B with smooth boundary in a smooth complete (possibly noncompact)…
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Local Hölder continuity of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry
For a complete noncompact connected Riemannian manifold with bounded geometry $$M^n$$Mn, we prove that the isoperimetric profile function $$I_{M^n}$$IMn is a locally $$(1-\frac{1}{n})$$(1-1n)-Hölder…
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The isoperimetric profile of a noncompact Riemannian manifold for small volumes
In the main theorem of this paper we treat the problem of existence of minimizers of the isoperimetric problem in a noncompact Riemannian manifold $$M$$, under the assumption of small volumes. We use…
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Sharp Isoperimetric Inequalities for Small Volumes in Complete Noncompact Riemannian Manifolds of Bounded Geometry Involving the Scalar Curvature
We provide an isoperimetric comparison theorem for small volumes in an $n$-dimensional Riemannian manifold $(M^n,g)$ with $C^3$ bounded geometry in a suitable sense involving the scalar curvature…
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The isoperimetric problem of a complete Riemannian manifold with a finite number of $C^0$‑asymptotically Schwarzschild ends
We show existence and caracterization of isoperimetric regions for large volumes, in C 0 -locally asymptotically Euclidean Riemannian manifolds with a finite number of C 0 -asymptotically…
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