6533b825fe1ef96bd12832df

RESEARCH PRODUCT

Isoperimetric inequality via Lipschitz regularity of Cheeger-harmonic functions

Renjin JiangRenjin JiangDachun YangPekka Koskela

subject

Applied MathematicsGeneral Mathematics010102 general mathematicsMathematical analysista111Poincaré inequalityIsoperimetric dimensionSpace (mathematics)Lipschitz continuity01 natural sciencesMeasure (mathematics)symbols.namesakeHarmonic function0103 physical sciencesMetric (mathematics)symbolsMathematics::Metric Geometry010307 mathematical physics0101 mathematicsIsoperimetric inequalityMathematics

description

Abstract Let ( X , d , μ ) be a complete, locally doubling metric measure space that supports a local weak L 2 -Poincare inequality. We show that optimal gradient estimates for Cheeger-harmonic functions imply local isoperimetric inequalities.

yearjournalcountryeditionlanguage
2014-05-01Journal de Mathématiques Pures et Appliquées
10.1016/j.matpur.2013.07.002http://juuli.fi/Record/0028569914