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

Shahroud Azami ()
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Shahroud Azami: Imam Khomeini International University

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 2, 477-488

Abstract: 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.

Keywords: 53E20; 53C40; 58C40; 35P15; Eigenvalues; Wentzell-Laplace operator; Geodesic curvature flow; Conformal (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-023-00493-0

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