What question did this study set out to answer?

The research focuses on the interaction between curvature and spectral invariants in compact Riemannian manifolds.

March 15, 2026Open Access

Spectral Geometry: Laplace–Beltrami Operator and Curvature Interaction

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Authors

DSDr. Mrinal Sarma

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Implication

This investigation reveals interactions between curvature and eigenvalues in compact Riemannian manifolds, indicating implications for spectral geometry and mathematical physics.

Key Points

The research focuses on the interaction between curvature and spectral invariants in compact Riemannian manifolds.
Analyzed the analytic structure of the Laplace–Beltrami operator.
Examined the asymptotic expansion of the heat kernel.
Studied eigenvalue estimates influenced by curvature bounds.
Discussed rigidity theorems and comparison principles linking geometric constraints with spectral behavior.
Identified connections between curvature and eigenvalues in spectral geometry.
Highlighted new developments in eigenvalue estimates and spectral rigidity.
Showcased applications in mathematical physics regarding curvature–spectrum interaction.

Cite This Study

Dr. Mrinal Sarma (2026) studied this question.

synapsesocial.com/papers/69b606ea83145bc643d1d5b8 https://doi.org/10.5281/zenodo.18997750

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Implication

This investigation reveals interactions between curvature and eigenvalues in compact Riemannian manifolds, indicating implications for spectral geometry and mathematical physics.

Spectral Geometry: Laplace–Beltrami Operator and Curvature Interaction

Discussion

Member takes

Implication

Key Points

Cite This Study

Spectral Geometry: Laplace–Beltrami Operator and Curvature Interaction

Discussion

Member takes

Implication

Key Points

Cite This Study

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