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The isoperimetric profile of a smooth Riemannian manifold for small volumes

- S. Nardulli
- Mathematics
- 7 October 2007

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,… Expand

A discontinuous isoperimetric profile for a complete Riemannian manifold

- S. Nardulli, P. Pansu
- Mathematics
- 16 June 2015

The first known example of a complete Riemannian manifold whose isoperimetric profile is discontinuous is given.

Generalized existence of isoperimetric regions in non-compact Riemannian manifolds and applications to the isoperimetric profile

- S. Nardulli
- Mathematics
- 4 October 2012

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… Expand

Existence of isoperimetric regions in non-compact Riemannian manifolds under Ricci or scalar curvature conditions

- A. Mondino, S. Nardulli
- Mathematics
- 1 October 2012

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… Expand

Continuity and differentiability properties of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry

- Abraham Enrique Muñoz Flores, S. Nardulli
- Mathematics
- 11 April 2014

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… Expand

Regularity of Isoperimetric Regions that are Close to a Smooth Manifold

- S. Nardulli
- Mathematics
- 1 June 2018

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)… Expand

Local Hölder continuity of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry

- Abraham Enrique Muñoz Flores, S. Nardulli
- MathematicsGeometriae Dedicata
- 16 June 2016

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… Expand

The isoperimetric profile of a noncompact Riemannian manifold for small volumes

- S. Nardulli
- Mathematics
- 2 September 2010

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… Expand

Sharp Isoperimetric Inequalities for Small Volumes in Complete Noncompact Riemannian Manifolds of Bounded Geometry Involving the Scalar Curvature

- S. Nardulli, Luis Eduardo Osorio Acevedo
- MathematicsInternational Mathematics Research Notices
- 5 November 2016

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… Expand

The isoperimetric problem of a complete Riemannian manifold with a finite number of $C^0$‑asymptotically Schwarzschild ends

- Abraham Enrique Muñoz Flores, S. Nardulli
- Mathematics
- 9 March 2015

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… Expand

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