Upper bounds for the first eigenvalue of the Laplace-Beltrami operator and an isoperimetric inequality for linked spheres
@inproceedings{Gage1978UpperBF, title={Upper bounds for the first eigenvalue of the Laplace-Beltrami operator and an isoperimetric inequality for linked spheres}, author={Michael E. Gage}, year={1978} }
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27 Citations
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The paper is devoted to the study of fine properties of the first eigenvalue on negatively curved spaces. First, depending on the parity of the space dimension, we provide asymptotically sharp…
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The fundamental gap of horoconvex domains in $\mathbb H^n$
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We show that, for horoconvex domains in the hyperbolic space, the product of their fundamental gap with the square of their diameter has no positive lower bound. The result follows from the study of…
The Vanishing of the Fundamental Gap of Convex Domains in
$$\mathbb {H}^n$$
H
n
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- 2021
For the Laplace operator with Dirichlet boundary conditions on convex domains in $$\mathbb H^n$$ H n , $$n\ge 2$$ n ≥ 2 , we prove that the product of the fundamental gap with the square of the…
Spectral multipliers on exponentially locally doubling metric measure spaces
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Let $$(X, \rho )$$(X,ρ) be a geodesic space endowed with a positive Borel measure $$\mu $$μ which satisfies an exponentially locally doubling condition. Assume that L is a nonnegative self-adjoint…
The Laplacian on Riemannian manifolds and some geometric estimates of its eigenvalues
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- 2018
1 The Hodge decomposition theorem 1 1.1 Motivating the Laplacian . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Defining the Laplacian for functions and forms . . . . . . . . . . . . . .…
A geometric approach to the modified milnor problem
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The Milnor Problem (modified) in the theory of group growth asks whether any finite presented group of vanishing algebraic entropy has at most polynomial growth. We show that a positive answer to the…
Volume comparison theorems for manifolds with radial curvature bounded
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In this paper, for complete Riemannian manifolds with radial Ricci or sectional curvature bounded from below or above, respectively, with respect to some point, we prove several volume comparison…