Geodesic
First $p$-Steklov eigenvalue under geodesic curvature flow
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 293-306

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We study the first nonzero $p$-Steklov eigenvalue on a two-dimensional compact Riemannian manifold with a smooth boundary along the geodesic curvature flow. We prove that the first nonzero $p$-Steklov eigenvalue is nondecreasing if the initial metric has positive geodesic curvature on boundary $\partial M$ and Gaussian curvature is identically equal to zero in $M$ along the un-normalized geodesic curvature flow. An eigenvalue estimation is also obtained along the normalized geodesic curvature flow.
Keywords: geodesic curvature, geodesic curvature flow.
Mots-clés : $p$-Steklov eigenvalue 
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     author = {A. Saha and S. Azami and S. K. Hui},
     title = {First $p${-Steklov} eigenvalue under geodesic curvature flow},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a17/}
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A. Saha; S. Azami; S. K. Hui. First $p$-Steklov eigenvalue under geodesic curvature flow. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 293-306. http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a17/