Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 43 min ago
PreprintarXiv licencearXiv

Harmonic-Einstein maps and critical metrics for eigenvalues of the conformal Laplacian

  • Mehdi Eddaoudi
Open at sourcePDFDOICite

Abstract

We prove that Clarke critical metrics for the ratio of the first two eigenvalues of the conformal Laplacian on a closed manifold with positive Yamabe constant correspond to harmonic--Einstein maps into a sphere. We discuss some rigidity consequences, as well as an extension to the higher-order GJMS operators.

Related

  1. Arithmetic classification of the Dirichlet eigenvalues for a one-dimensional nonlocal p-Laplacian problem
    Shingo Takeuchi
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv
  2. Eigenvalues and eigenfunctions of the fractional Laplacian on the interval
    Cheng Zhang
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsMathematical physicsarXiv
  3. On the Brouwer-type Conjecture for Signless Laplacian Eigenvalues of Graphs
    Ruisong Yuan, Xiao-Dong Zhang
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  4. The number of Laplacian eigenvalues of trees less than one
    Jiaxin Guo, Tao Hu, Quanyu Tang
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  5. Universality for the extreme eigenvalues of Laplacian random matrices
    Andrew Campbell, Kyle Luh, Sean O'Rourke
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@misc{eddaoudi2026harmoniceinstein,
  title = {{Harmonic-Einstein maps and critical metrics for eigenvalues of the conformal Laplacian}},
  author = {Mehdi Eddaoudi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28894},
  eprint = {2610.28894},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28894},
}
RIS
TY  - UNPB
TI  - Harmonic-Einstein maps and critical metrics for eigenvalues of the conformal Laplacian
AU  - Mehdi Eddaoudi
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28894
UR  - https://arxiv.org/abs/2610.28894
AB  - We prove that Clarke critical metrics for the ratio of the first two eigenvalues of the conformal Laplacian on a closed manifold with positive Yamabe constant correspond to harmonic--Einstein maps into a sphere. We discuss some rigidity consequences, as well as an extension to the higher-order GJMS operators.
ER  -