Stability of the second non trivial eigenvalue of the Neumann Laplacian

2024/05/30 by Liao, Xin
#47A75 #49Q20 #49R05 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2405.20050

Abstract

In this paper, building on the ideas of Brasco and Pratelli (Geom. Funct. Anal., 22 (2012), 107-135), we establish a stability estimate for Bucur and Henrot's inequality (Acta Math., 222 (2019), 337-361). Their inequality asserts that, among regular sets of given measure, the disjoint union of two balls with the same radius maximizes the second non trivial eigenvalue of the Neumann Laplacian. Last week I was informed of the same result of this paper has been published by Wang K, Wu H. A quantitative Bucur Henrot inequality. Mathematische Nachrichten, 2022, 295(12): 2436-2451. So thearticle has been deprecated.

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