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1890. Sharp spectral gap estimates for higher-order operators on Cartan-Hadamard manifolds
Invited abstract in session MD-41: Optimization on Geodesic Metric Spaces I: Smooth case, stream Optimization on Geodesic Metric Spaces: Smooth and Nonsmooth.
Monday, 14:30-16:00Room: 97 (building: 306)
Authors (first author is the speaker)
| 1. | Csaba Farkas
|
| Department of Mathematics and Informatics, Sapientia Hungarian University of Transylvania |
Abstract
The goal of this talk is to provide sharp spectral gap estimates for problems involving higher-order operators (including both the clamped and buckling plate problems) on Cartan-Hadamard manifolds. The proofs are symmetrization-free -- thus no sharp isoperimetric inequality is needed -- based on two general, yet elementary functional inequalities. The spectral gap estimate for clamped plates solves a sharp asymptotic problem from Cheng and Yang [Proc. Amer. Math. Soc., 2011] concerning the behavior of higher-order eigenvalues on hyperbolic spaces, and answers a question raised in Kristály [Adv. Math., 2020] on the validity of such sharp estimates in high-dimensional Cartan-Hadamard manifolds. As a byproduct of the general functional inequalities, various Rellich inequalities are established in the same geometric setting.
Keywords
- Non-smooth Optimization
Status: accepted
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