TY - JOUR
T1 - Gradient and Eigenvalue Estimates on the Canonical Bundle of Kähler Manifolds
AU - Lu, Zhiqin
AU - Zhang, Qi S.
AU - Zhu, Meng
N1 - Publisher Copyright:
© 2021, Mathematica Josephina, Inc.
PY - 2021/10
Y1 - 2021/10
N2 - We prove certain gradient and eigenvalue estimates, as well as the heat kernel estimates, for the Hodge Laplacian on (m, 0) forms, i.e., sections of the canonical bundle of Kähler manifolds, where m is the complex dimension of the manifold. Instead of the usual dependence on curvature tensor, our condition depends only on the Ricci curvature bound. The proof is based on a new Bochner type formula for the gradient of (m, 0) forms, which involves only the Ricci curvature and the gradient of the scalar curvature.
AB - We prove certain gradient and eigenvalue estimates, as well as the heat kernel estimates, for the Hodge Laplacian on (m, 0) forms, i.e., sections of the canonical bundle of Kähler manifolds, where m is the complex dimension of the manifold. Instead of the usual dependence on curvature tensor, our condition depends only on the Ricci curvature bound. The proof is based on a new Bochner type formula for the gradient of (m, 0) forms, which involves only the Ricci curvature and the gradient of the scalar curvature.
KW - Eigenvalue
KW - Gradient estimates
KW - Kahler manifold
UR - https://www.scopus.com/pages/publications/85102789803
U2 - 10.1007/s12220-021-00647-8
DO - 10.1007/s12220-021-00647-8
M3 - 文章
AN - SCOPUS:85102789803
SN - 1050-6926
VL - 31
SP - 10304
EP - 10335
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 10
ER -