Regularity of isoperimetric hypersurfaces in Riemannian manifolds

By Frank Morgan. 2003

170 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1c156c2e1e326c3e6d53437023ff273f186b1db7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Emanuel Milman
2. A. V. Kolesnikov
3. Jonathan J. Zhu
4. Xin Zhou
5. César Rosales
6. Manuel Ritor'e
7. Otis Chodosh
8. Marco A. M. Guaraco

In Astronomy and Astrophysics

1. César Rosales
2. A. V. Kolesnikov
3. Manuel Ritor'e
4. Jonathan J. Zhu
5. Xin Zhou
6. Emanuel Milman

In Geometry and Topology

1. A. V. Kolesnikov
2. Jonathan J. Zhu
3. Emanuel Milman
4. Xin Zhou
5. César Rosales
6. Manuel Ritor'e
7. Marco A. M. Guaraco
8. Antoine Song

Citations in the corpus

• Sharp Isoperimetric Inequalities and Model Spaces for Curvature-Dimension-Diameter Condition (2011, background): “5] and [72]) or Almgren [1] (whose approach was elucidated by Bombieri [19] and Morgan [60]); the extension to the manifold-with-density setting is due to Morgan [60, Remark 3.”
• Existence of hypersurfaces with prescribed mean curvature I – generic min-max (2018, background): “The following result about regularity of boundaries which minimize the Ah functional can be found in [47].”
• Existence and uniqueness of minimizers of general least gradient problems (2013, unknown): “(This is documented for example in [14].”
• Some Isoperimetric Problems in Planes with Density (2009, unknown): “Far from Γ, standard regularity holds [22].”
• Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones (2003, background): “so be stated in the setting of Riemannian manifolds, by using the paper of F. Almgren [A]. A complete proof of interior regularity for isoperimetric boundaries in Riemannian manifolds can be found in [M1]; weaker regularity properties when ∂Mis not C∞, but only C1,1, are also established. We collect”
• Brascamp–Lieb-Type Inequalities on Weighted Riemannian Manifolds with Boundary (2013, unknown): “ and so the assertion follows. We remark that the results in [41] were proved assuming the metric in question is C∞ smooth, but an inspection of the proof, which builds upon the regularity results in [47], verifies that it is enough to have a C2 metric, so the results are indeed applicable to (∂M,g0,”
• Poincaré and Brunn-Minkowski inequalities on the boundary of weighted Riemannian manifolds (2017, background): “10 were obtained assuming the metric in question is C∞ smooth, but an inspection of the proof, which builds upon the regularity results in [56], verifies that it is enough to have a C2 metric.”
• On the role of convexity in isoperimetry, spectral gap and concentration (2007, methodology): “This was also formally verified by Morgan and Johnson [73, Section 2.1 and Proposition 3.3].”
• GLOBAL PROPERTIES OF CONSTANT MEAN CURVATURE SURFACES IN H 2 ◊R (2006, unknown): “The regularity follows from [Morgan 2003].”