Sharp spectral gaps on metric measure spaces

In this paper, we extend the sharp lower bounds of spectral gap, due to Andrews-Clutterbuck (Anal PDE 6(5):1013–1024, 2013 ), Bakry-Qian (Adv Math 155:98–153, 2000 ), Chen-Wang (Sci Sin A 37:1–14, 1994 ) and Chen-Wang (Sci Sin A 40:384-394, 1997 ), from smooth Riemannian manifolds to general metric...

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Veröffentlicht in:	Calculus of variations and partial differential equations 2016-02, Vol.55 (1), p.1-14, Article 14
Hauptverfasser:	Jiang, Yin, Zhang, Hui-Chun
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Calculus of variations Calculus of Variations and Optimal Control Optimization Control Curvature Formulas (mathematics) Lower bounds Manifolds Mathematical analysis Mathematical and Computational Physics Mathematics Mathematics and Statistics Partial differential equations Riemann manifold Spectra Systems Theory Texts Theoretical
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Zusammenfassung:	In this paper, we extend the sharp lower bounds of spectral gap, due to Andrews-Clutterbuck (Anal PDE 6(5):1013–1024, 2013 ), Bakry-Qian (Adv Math 155:98–153, 2000 ), Chen-Wang (Sci Sin A 37:1–14, 1994 ) and Chen-Wang (Sci Sin A 40:384-394, 1997 ), from smooth Riemannian manifolds to general metric measure spaces with Riemannian curvature-dimension condition R C D ∗ ( K , N ) .
ISSN:	0944-2669 1432-0835
DOI:	10.1007/s00526-016-0952-4