TY - JOUR AU - Connor Anderson AU - Xavier Ramos Olivé AU - Kamryn Spinelli PY - 2021/11/08 Y2 - 2024/03/28 TI - Manifolds With Bounded Integral Curvature and no Positive Eigenvalue Lower Bounds JF - The PUMP Journal of Undergraduate Research JA - PUMP J. Undergrad. Res. VL - 4 IS - 0 SE - Articles DO - 10.46787/pump.v4i0.2572 UR - https://journals.calstate.edu/pump/article/view/2572 AB - 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. ER -