arXiv Analytics

Sign in

arXiv:1704.06384 [math.DG]AbstractReferencesReviewsResources

Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian

Shin Nayatani, Toshihiro Shoda

Published 2017-04-21Version 1

Jakobson-Levitin-Nadirashvili-Nigam-Polterovich conjectured that a certain singular metric on the Bolza surface, with area normalized, maximizes the first eigenvalue of the Laplacian. In this note, we announce that this conjecture is true, and outline the proof.

Comments: 9 pages, 3 figures
Categories: math.DG
Subjects: 58J50, 53A10
Related articles: Most relevant | Search more
arXiv:1405.0542 [math.DG] (Published 2014-05-03)
A note on lower bounds for the first eigenvalue of the Witten-Laplacian
arXiv:1610.00374 [math.DG] (Published 2016-10-03)
Estimates for the first eigenvalue of Jacobi operator on hypersurfaces
arXiv:1503.08493 [math.DG] (Published 2015-03-29)
Upper bounds for the first eigenvalue of the Laplacian on non-orientable surfaces

Links

Toolbox