Manifolds With Bounded Integral Curvature and no Positive Eigenvalue Lower Bounds
Keywords:
Laplace eigenvalue; integral Ricci curvature; dumbbell surfaces
Abstract
We provide an explicit construction of a sequence of closed surfaces with uniform bounds on the diameter and on Lp norms of the curvature, but without a positive lower bound on the first non-zero eigenvalue of the Laplacian λ1. This example shows that the assumption of smallness of the Lp norm of the curvature is a necessary condition to derive Lichnerowicz and Zhong-Yang type estimates under integral curvature conditions.
Published
2021-11-08
How to Cite
Anderson, C., Ramos Olivé, X., & Spinelli, K. (2021). Manifolds With Bounded Integral Curvature and no Positive Eigenvalue Lower Bounds. The PUMP Journal of Undergraduate Research, 4, 222-235. Retrieved from https://journals.calstate.edu/pump/article/view/2572
Section
Articles
Copyright (c) 2021 Connor Anderson, Xavier Ramos Olivé, Kamryn Spinelli

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