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Evolution of eigenvalue of the Wentzell-Laplace operator along the geodesic curvature flow

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Abstract

In this paper, we study continuity, differentiability and monotonicity for the first nonzero eigenvalue of the Wentzell-Laplace operator along the geodesic curvature flow on two-dimensional compact manifolds with boundary. In especial, we show that the first nonzero eigenvalue of the Wentzell-Laplace operator is monotonic under the geodesic curvature flow and we find some monotonic quantities dependent to the first nonzero eigenvalue along the geodesic curvature flow.

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Authors and Affiliations

  1. Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran

    Shahroud Azami

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  1. Shahroud Azami
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Correspondence to Shahroud Azami.

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Communicated by K Sandeep.

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Azami, S. Evolution of eigenvalue of the Wentzell-Laplace operator along the geodesic curvature flow. Indian J Pure Appl Math (2023). https://doi.org/10.1007/s13226-023-00493-0

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  • DOI: https://doi.org/10.1007/s13226-023-00493-0

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