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
SN - 0926-2245
VL - 45
SP - 23
EP - 42
JO - Differential Geometry and its Applications
JF - Differential Geometry and its Applications
ER -