An upper bound for the first positive eigenvalue of the Kohn Laplacian on Reinhardt real hypersurfaces

Gian Maria Dall'Ara, Duong Ngoc Son

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

A real hypersurface in C 2 is said to be Reinhardt if it is invariant under the standard T 2-action on C 2. Its CR geometry can be described in terms of the curvature function of its “generating curve”, i.e., the logarithmic image of the hypersurface in the plane R 2. We give a sharp upper bound for the first positive eigenvalue of the Kohn Laplacian associated to a natural pseudohermitian structure on a compact and strictly pseudoconvex Reinhardt real hypersurface having closed generating curve (which amounts to the T 2action being free). Our bound is expressed in terms of the L 2-norm of the curvature function of the generating curve and is attained if and only if the curve is a circle.

OriginalspracheEnglisch
Seiten (von - bis)123-133
Seitenumfang11
FachzeitschriftProceedings of the American Mathematical Society
Jahrgang151
Ausgabenummer1
DOIs
PublikationsstatusVeröffentlicht - 2023

ÖFOS 2012

  • 101008 Funktionentheorie

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