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      Lower bounds for the first eigenvalue of the Laplacian on K\"ahler manifolds

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          Abstract

          We establish lower bound for the first nonzero eigenvalue of the Laplacian on a closed K\"ahler manifold in terms of dimension, diameter, and lower bounds of holomorphic sectional curvature and orthogonal Ricci curvature. On compact K\"ahler manifolds with boundary, we prove lower bounds for the first nonzero Neumann or Dirichlet eigenvalue in terms of geometric data. Our results are K\"ahler analogues of well-known results for Riemannian manifolds.

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          Author and article information

          Journal
          24 October 2020
          Article
          2010.12792
          e8b96b61-ed70-498e-a5af-7af338a81554

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          35P15, 53C55
          Comments are welcome
          math.DG math.AP math.SP

          Analysis,Functional analysis,Geometry & Topology
          Analysis, Functional analysis, Geometry & Topology

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