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^*

^*Corresponding author for this work

Max Planck Institute for Mathematics in the Sciences (MIS)

Research output: Contribution to journal › Article › Research › 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).

Original language	English
Pages (from-to)	107-113
Number of pages	7
Journal	Calculus of Variations and Partial Differential Equations
Volume	14
Issue number	1
DOIs	https://doi.org/10.1007/s005260100095
Publication status	Published - 1 Jan 2002
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1007/s005260100095

Cite this

@article{7caad0f6444841298947eb6837ddaab0,

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

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 Eigk (n + 1 - k) and Eigk-1 (n + 1 - κ) are at least of dimension (nκ).",

author = "Knut Smoczyk",

year = "2002",

month = jan,

day = "1",

doi = "10.1007/s005260100095",

language = "English",

volume = "14",

pages = "107--113",

journal = "Calculus of Variations and Partial Differential Equations",

issn = "0944-2669",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Note on the spectrum of the Hodge-Laplacian for κ-forms on minimal Legendre submanifolds in S2n+1

AU - Smoczyk, Knut

PY - 2002/1/1

Y1 - 2002/1/1

N2 - 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 Eigk (n + 1 - k) and Eigk-1 (n + 1 - κ) are at least of dimension (nκ).

AB - 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 Eigk (n + 1 - k) and Eigk-1 (n + 1 - κ) are at least of dimension (nκ).

UR - https://www.scopus.com/pages/publications/0036461838

U2 - 10.1007/s005260100095

DO - 10.1007/s005260100095

M3 - Article

AN - SCOPUS:0036461838

SN - 0944-2669

VL - 14

SP - 107

EP - 113

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 1