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Spectral geometry: old questions and new answers — arXiv:2609.28602

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.28602
License (as archived): CC0-1.0
Archived: 2026-10-08T02:56:39.596Z
SHA-256 of the archived text: 6f935aad6019b3b503f02a8b686d1dfa54fe16c4c42574404ec2f4ea47da05a8
Stable URL of this page: https://metraipolis.com/documento/dc_451f96dcfbf5

How to cite

Spectral geometry: old questions and new answers — arXiv:2609.28602 — arXiv (en), https://arxiv.org/abs/2609.28602 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_451f96dcfbf5 (Metraipolis archive dc_451f96dcfbf5, sha256 6f935aad6019b3b503f02a8b686d1dfa54fe16c4c42574404ec2f4ea47da05a8)

BibTeX

@misc{dc451f96dcfbf5,
  title = {Spectral geometry: old questions and new answers — arXiv:2609.28602},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.28602},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_451f96dcfbf5; sha256 6f935aad6019b3b503f02a8b686d1dfa54fe16c4c42574404ec2f4ea47da05a8},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.28602. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

These are extended notes based on a series of lectures given by the author at the Institut de Mathematiques de Toulouse in June 2025. The goal is to present classical problems as well as the most recent developments in spectral geometry of the Laplace operator in Euclidean domains, subject to Dirichlet, Neumann and Robin boundary conditions. Among the topics covered, there are embedded eigenvalues in unbounded domains, spectral isoperimetric inequalities, nodal-line and hot-spots conjectures, inverse problems of hearing the shape of a drum and geometrically induced eigenvalues and Hardy-type inequalities in curved tubes.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-28 in math.OC).
Categorie arXiv: Spectral Theory (math.SP) ; Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2609.28602 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T02:20:09.754Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-28?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).