Note on the spectrum of the Hodge-Laplacian for κ-forms on minimal Legendre submanifolds in S2n+1

Knut Smoczyk

doi:10.1007/s005260100095

Note on the spectrum of the Hodge-Laplacian for κ-forms on minimal Legendre submanifolds in S²ⁿ⁺¹

Knut Smoczyk^*

^*Korrespondierende*r Autor*in für diese Arbeit

Max-Planck-Institut für Mathematik in den Naturwissenschaften (MIS)

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Abstract

Given a minimal Legendre immersion L in S²ⁿ⁺¹ and n ≥ k ≥ 1 we prove that n + 1 - κk is an eigenvalue of the Hodge-Laplacian acting on κ and (κ - 1)-forms on L. In particular we show that the eigenspaces Eig_k (n + 1 - k) and Eig_k-1 (n + 1 - κ) are at least of dimension (ⁿ_κ).

Originalsprache	Englisch
Seiten (von - bis)	107-113
Seitenumfang	7
Fachzeitschrift	Calculus of Variations and Partial Differential Equations
Jahrgang	14
Ausgabenummer	1
DOIs	https://doi.org/10.1007/s005260100095
Publikationsstatus	Veröffentlicht - 1 Jan. 2002
Extern publiziert	Ja

ASJC Scopus Sachgebiete

Analysis
Angewandte Mathematik

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10.1007/s005260100095

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