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math.AP2014
Monotonicity of the first Dirichlet eigenvalue of the Laplacian on manifolds of nonpositive curvature
Tom Carroll, Jesse Ratzkin
Let be a complete manifold of nonpositive scalar curvature, let be a suitable domain, and let be the first Dirichlet eigenvalue of the Laplace-Beltrami…
math.AP2014
A reverse Holder inequality for extremal Sobolev functions
Tom Carroll, Jesse Ratzkin
Let , let be a bounded domain with smooth boundary, and let . We prove a reverse-Holder inequality for functions realizing th…