Generic simplicity of ellipses

Q: What does this research mean for the field?

Except for a countable set of eccentricities, the spectrum of the Laplace operator in an ellipse with either Dirichlet or Neumann boundary conditions is simple. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Luc Hillairet; Chris Judge

doi:10.4171/jst/622

July 27, 2026Journal of Spectral TheoryOpen Access

Generic simplicity of ellipses

View Full Paper

Ask AI

Bookmark

Share

Key Points

The aim is to investigate the behavior of the Laplace operator in ellipses with different boundary conditions.
Examined the Laplace operator on ellipses with Dirichlet and Neumann boundary conditions.
Proved simplicity of the spectrum, excluding a countable set of eccentricities.
Demonstrated that the spectrum is simple for most eccentricities.
Identified that only a countable set of eccentricities leads to complexity in the spectrum.

Implication

Proves the simplicity of the spectrum in ellipses, suggesting a unique mathematical behavior in specific conditions.

Abstract

We study the Laplace operator in an ellipse with either Dirichlet or Neumann boundary. We prove that except for a countable set of eccentricities, the spectrum is simple.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Hillairet et al. (2026) studied this question.

synapsesocial.com/papers/6a6af4ad60e2b924d3ea02a6 https://doi.org/10.4171/jst/622

View Full Paper

Ask AI

Bookmark

Share

Generic simplicity of ellipses

Key Points

Implication

Abstract

Discussion

Cite This Study

Generic simplicity of ellipses

Key Points

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading