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Geometric estimates on weighted p-fundamental tone and applications to the first eigenvalue of submanifolds with bounded mean curvature
journal contribution
posted on 2023-06-09, 23:25 authored by Abimbola Abolarinwa, Ali TaheriAli TaheriThis paper generalizes to the context of smooth metric measure spaces and submanifolds with negative sectional curvatures some well-known geometric estimates on the p-fundamental tone by using vector fields satisfying a positive divergence condition. Choosing the vector field to be the gradient of an appropriately chosen distance function yields generalised McKean estimates whilst other choices of vector fields yield new geometric estimates generalising certain results of Lima et al. (Nonlinear Anal. 2010;72:771–781). We also obtain a lower bound on the spectrum of the weighted p-Laplacian on a complete noncompact smooth metric space with the underlying space being a submanifold with bounded mean curvature in the hyperbolic space form of constant negative sectional curvature generalising results of Du and Mao (J Math Anal Appl. 2017;456:787–795).
History
Publication status
- Published
File Version
- Accepted version
Journal
Complex Variables and Elliptic Equations: an international journalISSN
1747-6933Publisher
Taylor & FrancisExternal DOI
Issue
6Volume
67Page range
1379-1392Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Analysis and Partial Differential Equations Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2021-03-25First Open Access (FOA) Date
2022-01-22First Compliant Deposit (FCD) Date
2021-03-25Usage metrics
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