Calibrations and Isoperimetric Profiles

We equip many noncompact nonsimply connected surfaces with smooth Riemannian metrics whose isoperimetric profile is smooth, a highly nongeneric property. The computation of the profile is based on a calibration argument, a rearrangement argument, the Bol-Fiala curvature dependent inequality, togethe...

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Bibliographic Details
Published in:American journal of mathematics 2007-04, Vol.129 (2), p.315-350
Main Authors: Grimaldi, Renata, Pansu, Pierre
Format: Article
Language:English
Subjects:
Calculus of variations and optimal control
Calibration
Critical points
Critical values
Curvature
Differential Geometry
Exact sciences and technology
Geometry
Mathematical analysis
Mathematical functions
Mathematical problems
Mathematical surfaces
Mathematics
Radius of curvature
Riemann manifold
Rotation
Sciences and techniques of general use
Surfaces of revolution
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Summary:We equip many noncompact nonsimply connected surfaces with smooth Riemannian metrics whose isoperimetric profile is smooth, a highly nongeneric property. The computation of the profile is based on a calibration argument, a rearrangement argument, the Bol-Fiala curvature dependent inequality, together with new results on the profile of surfaces of revolution and some hardware know-how.
ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.2007.0010