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Eigenvalue bounds for Schrödinger operators with complex potentials on compact manifolds

  • Jean-Claude Cuenin ORCID logo EMAIL logo
Veröffentlicht/Copyright: 1. August 2025
Forum Mathematicum
Aus der Zeitschrift Forum Mathematicum

Abstract

We prove eigenvalue bounds for Schrödinger operator - Δ g + V on compact manifolds with complex potentials V. The bounds depend only on an L q -norm of the potential, and they are shown to be optimal, in a certain sense, on the round sphere and more general Zoll manifolds. These bounds are natural analogues of Frank’s [R. L. Frank, Eigenvalue bounds for Schrödinger operators with complex potentials, Bull. Lond. Math. Soc. 43 2011, 4, 745–750] results in the Euclidean case.

MSC 2020: 58J50; 35P15; 31Q12

Communicated by Christopher D. Sogge


Award Identifier / Grant number: EP/X011488/1

Funding statement: Support through the Engineering & Physical Sciences Research Council (EP/X011488/1) is acknowledged.

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Received: 2024-12-10
Revised: 2025-06-22
Published Online: 2025-08-01

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