A simple proof of an isoperimetric inequality for Euclidean and hyperbolic cone-surfaces

DOI10.1016/j.difgeo.2015.09.007zbMath1329.52009arXiv1409.7681OpenAlexW2962758624WikidataQ115355834 ScholiaQ115355834MaRDI QIDQ891588

Ivan Izmestiev

Publication date: 17 November 2015

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.7681

zbMATH Keywords

isoperimetric inequalitydiscrete conformal deformationEuclidean and hyperbolic cone-metrics

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Global differential geometry (53C99)

Related Items (7)

Signature Calculation of the Area Hermitian Form on Some Spaces of Polygons ⋮ An isoperimetric inequality for planar triangulations ⋮ Functionals with extrema at reproducing kernels ⋮ Ideal triangulation and disc unfolding of a singular flat surface ⋮ Contraction property of certain classes of log-\(\mathcal{M}\)-subharmonic functions in the unit ball ⋮ A Faber–Krahn inequality for Wavelet transforms ⋮ Geometry and entropies in a fixed conformal class on surfaces

Cites Work

• Discrete conformal variations and scalar curvature on piecewise flat two- and three-dimensional manifolds
• A sharp four dimensional isoperimetric inequality
• An isoperimetric comparison theorem
• Problèmes isoperimetriques et espaces de Sobolev
• The Cartan-Hadamard conjecture and the little prince
• Discrete conformal maps and ideal hyperbolic polyhedra
• Le problème des isoperimetres sur les surfaces ouvertes à courbure positive
• The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature
• COMBINATORIAL YAMABE FLOW ON SURFACES
• Subharmonic Functions and Surfaces of Negative Curvature
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