Detang Zhou

activity

20242026

collaborators

5 papers

math.DG2026

Eigenvalue Estimates for SchrÃ¶dinger Operators on Ricci Shrinkers

Xu Cheng, Franciele Conrado, Neilha Pinheiro +1

Let $(M, g, f, I ¨ )$ be a complete Ricci shrinker satisfying $Ric + \nabla^{2} f = \frac{g}{2 I ¨ }$ and let $R$ denote its scalar curvature. For a confined function $V$ on $M$ , we o…

math.DG2026

Rigidity of compact quasi-Einstein manifolds with boundary

Johnatan Costa, Ernani Ribeiro, Detang Zhou

In this article, we investigate the geometry of compact quasi-Einstein manifolds with boundary. We show that a $3$ -dimensional simply connected compact quasi-Einstein manifold with…

math.DG2025

An eigenvalue estimate for self-shrinkers in a Ricci shirinker

Franciele Conrado, Detang Zhou

In this paper, we study the drifted Laplacian $I^_{f}$ on a hypersurface $M$ in a Ricci shrinker $(M, g, f)$ . We prove that the spectrum of $I^_{f}$ is discrete for immersed h…

math.DG2024

Spectrum of the drift Laplacian on Ricci expanders

Helton Leal, Matheus Vieira, Detang Zhou

In this paper, we study the spectrum of the drift Laplacian on Ricci expanders. We show that the spectrum is discrete when the potential function is proper, and we show that the hy…

math.DG2024

A lower bound for the first eigenvalue of a minimal hypersurface in the sphere

Let $I^£$ be a closed embedded minimal hypersurface in the unit sphere $S^{m + 1}$ and let $I^ = I^max £∣ A ∣$ be the norm of its second fundamental form. In this work we…