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The research explores the relationship between curvature and spectral properties of differential operators in geometry.

March 15, 2026Open Access

Spectral Geometry: Laplace–Beltrami Operator and Curvature Interaction

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Reveals the interaction between curvature and eigenvalues in compact Riemannian manifolds, suggesting implications for spectral analysis.

The research explores the relationship between curvature and spectral properties of differential operators in geometry.
Analyze the Laplace–Beltrami operator on compact Riemannian manifolds
Study the asymptotic expansion of the heat kernel
Discuss rigidity theorems and comparison principles connecting geometry with spectrum
Investigate curvature-dependent inequalities and spectral comparison theorems
Establish a connection between eigenvalues and geometric features such as curvature
Highlight recent advancements in eigenvalue estimates and spectral rigidity
Provide a unified overview of the interaction between curvature and the spectral properties of manifolds

Dr. Mrinal Sarma (2026) studied this question.

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