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arXiv · 2609.02104

Conformal Ricci Curvature and Spectral Estimates

Xiaoshang Jin
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Abstract

We derive optimized upper bounds for the first Dirichlet eigenvalue of a bounded domain under lower bounds for the conformal Ricci tensor of Shen and Ye. The method also yields sharp estimates for the bottom spectrum on complete noncompact manifolds, a four-dimensional application involving $Q$-curvature, and local and global spectral-Ricci extensions of Cheng's estimate. As a consequence, we obtain a sharp comparison between the spectra of the Laplacian and the conformal Laplacian in terms of the smallest Schouten eigenvalue.

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Xiaoshang Jin. 2026-09-02. Conformal Ricci Curvature and Spectral Estimates. https://arxiv.org/abs/2609.02104

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