TY - JOUR

T1 - Lower bound estimates for the first eigenvalue of the weighted p-Laplacian on smooth metric measure spaces

AU - Wang, Yu-Zhao

AU - Li, Huai-Qian

PY - 2016/4

Y1 - 2016/4

N2 - New lower bounds of the first nonzero eigenvalue of the weighted p-Laplacian are established on compact smooth metric measure spaces with or without boundaries. Under the assumption of positive lower bound for the m-Bakry-Émery Ricci curvature, the Escobar-Lichnerowicz-Reilly type estimates are proved; under the assumption of nonnegative ∞-Bakry-Émery Ricci curvature and the m-Bakry-Émery Ricci curvature bounded from below by a non-positive constant, the Li-Yau type lower bound estimates are given. The weighted p-Bochner formula and the weighted p-Reilly formula are derived as the key tools for the establishment of the above results.

AB - New lower bounds of the first nonzero eigenvalue of the weighted p-Laplacian are established on compact smooth metric measure spaces with or without boundaries. Under the assumption of positive lower bound for the m-Bakry-Émery Ricci curvature, the Escobar-Lichnerowicz-Reilly type estimates are proved; under the assumption of nonnegative ∞-Bakry-Émery Ricci curvature and the m-Bakry-Émery Ricci curvature bounded from below by a non-positive constant, the Li-Yau type lower bound estimates are given. The weighted p-Bochner formula and the weighted p-Reilly formula are derived as the key tools for the establishment of the above results.

KW - eigenvalue estimate

KW - Bakry–Émery Ricci curvature

KW - smooth metric measure space

KW - weighted p-Bochner formula

KW - weighted p-Laplacian

KW - weighted p-Reilly formula

UR - http://purl.org/au-research/grants/arc/DP130101302

UR - http://www.scopus.com/inward/record.url?scp=84950262094&partnerID=8YFLogxK

U2 - 10.1016/j.difgeo.2015.11.008

DO - 10.1016/j.difgeo.2015.11.008

M3 - Article

VL - 45

SP - 23

EP - 42

JO - Differential Geometry and its Applications

JF - Differential Geometry and its Applications

SN - 0926-2245

ER -