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February 16, 2026Semigroup ForumOpen Access

The spectrum of the Laplacian on closed manifolds and the heat asymptotics near conical points

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Authors

NRNikolaos Roidos

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Overview

Finds an asymptotic expansion of heat solutions on manifolds, indicating insights into Laplacian spectra.

Key Points

  • The research aims to examine the relationship between the spectrum of the Laplacian on closed manifolds and the heat asymptotics near conical points.
  • Analyzed a smooth, closed manifold endowed with a Riemannian metric.
  • Considered the homogeneous heat equation on an $(n+1)$-dimensional manifold with boundary.
  • Derived an arbitrary long asymptotic expansion of solutions to the heat equation as 'x' approaches zero.
  • The spectrum of the Laplacian on the manifold determines the asymptotic expansion of the heat equation solutions.
  • The findings suggest a reciprocal relationship between the Laplacian spectrum and asymptotic expansion characteristics.

Cite This Study

Nikolaos Roidos (2026) studied this question.

synapsesocial.com/papers/6992b4ad9b75e639e9b09a0ehttps://doi.org/10.1007/s00233-026-10617-7
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