Existence of metrics maximizing the first eigenvalue on non-orientable surfaces

2017/03/03 by Matthiesen, Henrik, Siffert, Anna
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1703.01264

Abstract

We prove the existence of metrics maximizing the first eigenvalue normalized by area on closed, non-orientable surfaces assuming two spectral gap conditions. These spectral gap conditions are proved by the authors in \citeMS3.

Related

• Existence of metrics maximizing the first Laplace eigenvalue on closed surfaces
• Maximal metrics for the first Steklov eigenvalue on surfaces
• Existence and regularity of maximal metrics for the first Laplace eigenvalue on surfaces
• Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian
• Geometric spectral optimization on surfaces