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Sub-Laplacian Comparison Theorem and Gradient Estimates on Complete Noncompact Contact Riemannian Manifolds
Abstract
In this paper, we first derive the Bochner-type formulas of the Hermitian-Tanno connection on contact Riemannian manifolds. Second, we prove a sub-Laplacian comparison theorem on complete noncompact contact Riemannian manifolds with bounded geometric conditions. Finally, we obtain the gradient estimates of a positive eigenfunction on a complete noncompact contact Riemannian manifold which satisfies similar geometric conditions.
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BibTeX
@misc{yang2026sublaplacian,
title = {{Sub-Laplacian Comparison Theorem and Gradient Estimates on Complete Noncompact Contact Riemannian Manifolds}},
author = {Guilin Yang and Biqiang Zhao and Weihao Zheng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31720},
eprint = {2610.31720},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31720},
}
RIS
TY - UNPB
TI - Sub-Laplacian Comparison Theorem and Gradient Estimates on Complete Noncompact Contact Riemannian Manifolds
AU - Guilin Yang
AU - Biqiang Zhao
AU - Weihao Zheng
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31720
UR - https://arxiv.org/abs/2610.31720
AB - In this paper, we first derive the Bochner-type formulas of the Hermitian-Tanno connection on contact Riemannian manifolds. Second, we prove a sub-Laplacian comparison theorem on complete noncompact contact Riemannian manifolds with bounded geometric conditions. Finally, we obtain the gradient estimates of a positive eigenfunction on a complete noncompact contact Riemannian manifold which satisfies similar geometric conditions.
ER -