First eigenvalue of the Laplacian of a geodesic ball and area-based symmetrization of its metric tensor
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Mostrar el registro completo del ítemcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Título
First eigenvalue of the Laplacian of a geodesic ball and area-based symmetrization of its metric tensorFecha de publicación
2022Editor
ElementISSN
1846-579XCita bibliográfica
Gimeno, V., & Sarrion-Pedralva, E. (2021). First Eigenvalue of the Laplacian of a Geodesic Ball and Area-Based Symmetrization of its Metric Tensor. arXiv preprint arXiv:2103.17134.Tipo de documento
info:eu-repo/semantics/articleVersión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
Given a Riemmanian manifold, we provide a new method to compute a sharp upper
bound for the first eigenvalue of the Laplacian for the Dirichlet problem on a geodesic ball of
radius less than the injectivity radius ... [+]
Given a Riemmanian manifold, we provide a new method to compute a sharp upper
bound for the first eigenvalue of the Laplacian for the Dirichlet problem on a geodesic ball of
radius less than the injectivity radius of the manifold. This upper bound is obtained by transforming the metric tensor into a rotationally symmetric metric tensor that preserves the area of
the geodesic spheres. The provided upper bound can be computed using only the area function
of the geodesic spheres contained in the geodesic ball and it is sharp in the sense that the first
eigenvalue of geodesic ball coincides with our upper bound if and only if the mean curvature
pointed inward of each geodesic sphere is a radial function. [-]
Publicado en
Journal of Mathematical Inequalities. Volume 16, Number 1 (2022), 371–391Entidad financiadora
Universitat Jaume I | Ministerio de Economía, Industria y Competitividad | Generalitat Valenciana
Código del proyecto o subvención
UJI-B2018-35 | MTM2017-84851-C2-2-P | PID2020-115930GA-I00 | MCIN/ AEI /10.13039/501100011033 | ACIF-2019-096
Derechos de acceso
© Element, Zagreb
Paper JMI-16-28
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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