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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Lower bounds for the first eigenvalue of the Laplacian on Kähler manifolds
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by Xiaolong Li and Kui Wang PDF
Trans. Amer. Math. Soc. 374 (2021), 8081-8099 Request permission

Abstract:

We establish lower bound for the first nonzero eigenvalue of the Laplacian on a closed Kähler manifold in terms of dimension, diameter, and lower bounds of holomorphic sectional curvature and orthogonal Ricci curvature. On compact Kähler manifolds with boundary, we prove lower bounds for the first nonzero Neumann or Dirichlet eigenvalue in terms of geometric data. Our results are Kähler analogues of well-known results for Riemannian manifolds.
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Additional Information
  • Xiaolong Li
  • Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada
  • Address at time of publication: Department of Mathematics, Statistics and Physics, Wichita State University, Wichita, Kansas, 67260
  • ORCID: 0000-0002-0932-8374
  • Email: li1304@mcmaster.ca
  • Kui Wang
  • Affiliation: School of Mathematical Sciences, Soochow University, Suzhou, 215006, People’s Republic of China
  • Email: kuiwang@suda.edu.cn
  • Received by editor(s): October 1, 2020
  • Received by editor(s) in revised form: March 12, 2021
  • Published electronically: August 30, 2021
  • Additional Notes: The research of the second author was supported by NSFC No.11601359

  • Dedicated: Dedicated to Professor Richard Schoen on the occasion of his 70th birthday
  • © Copyright 2021 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 374 (2021), 8081-8099
  • MSC (2020): Primary 35P15, 53C55
  • DOI: https://doi.org/10.1090/tran/8434
  • MathSciNet review: 4328692