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October 2, 2025Open Access

Logarithmic Laplacian on General Riemannian Manifolds

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Explicit pointwise integral formulas for logarithmic laplacian under a Ricci lower bound show deep connections to geometric analysis.
The study compares traditional spectral definitions with heat kernel definitions, revealing significant mathematical discrepancies.
Using sharp heat kernel asymptotics on hyperbolic space, we improve estimates for both fractional and logarithmic kernels.
Identification of the optimal domain for logarithmic laplacian establishes its continuity in Lp spaces, enhancing geometric understanding.

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This work defines logarithmic Laplacian on Riemannian manifolds, highlighting links to fractional Laplacians and spectral theory.

Rui Chen (2025) studied this question.

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