Curvature Dimension Inequalities and Subelliptic Heat Kernel Gradient Bounds on Contact Manifolds

TY - JOUR

T1 - Curvature Dimension Inequalities and Subelliptic Heat Kernel Gradient Bounds on Contact Manifolds

AU - Baudoin, Fabrice

AU - Wang, Jing

PY - 2014/2

Y1 - 2014/2

N2 - We study curvature dimension inequalities for the sub-Laplacian on contact Riemannian manifolds. This new curvature dimension condition is then used to obtain: • Geometric conditions ensuring the compactness of the underlying manifold (Bonnet-Myers type results); • Volume estimates of metric balls; • Gradient bounds and stochastic completeness for the heat semigroup generated by the sub-Laplacian; • Spectral gap estimates.

AB - We study curvature dimension inequalities for the sub-Laplacian on contact Riemannian manifolds. This new curvature dimension condition is then used to obtain: • Geometric conditions ensuring the compactness of the underlying manifold (Bonnet-Myers type results); • Volume estimates of metric balls; • Gradient bounds and stochastic completeness for the heat semigroup generated by the sub-Laplacian; • Spectral gap estimates.

KW - Bochner's formula

KW - Contact manifold

KW - Curvature dimension inequality

KW - Gradient bounds for the heat semigroup

UR - http://www.scopus.com/inward/record.url?scp=84892680740&partnerID=8YFLogxK

U2 - 10.1007/s11118-013-9345-x

DO - 10.1007/s11118-013-9345-x

M3 - Journal article

AN - SCOPUS:84892680740

SN - 0926-2601

VL - 40

SP - 163

EP - 193

JO - Potential Analysis

JF - Potential Analysis

IS - 2

ER -