First eigenvalue of the Laplacian of a geodesic ball and area-based symmetrization of its metric tensor
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Títol
First eigenvalue of the Laplacian of a geodesic ball and area-based symmetrization of its metric tensorData de publicació
2022Editor
ElementISSN
1846-579XCita bibliogràfica
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.Tipus de document
info:eu-repo/semantics/articleVersió
info:eu-repo/semantics/publishedVersionParaules clau / Matèries
Resum
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. [-]
Publicat a
Journal of Mathematical Inequalities. Volume 16, Number 1 (2022), 371–391Entitat finançadora
Universitat Jaume I | Ministerio de Economía, Industria y Competitividad | Generalitat Valenciana
Codi del projecte o subvenció
UJI-B2018-35 | MTM2017-84851-C2-2-P | PID2020-115930GA-I00 | MCIN/ AEI /10.13039/501100011033 | ACIF-2019-096
Drets d'accés
© Element, Zagreb
Paper JMI-16-28
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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