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Currently displaying 1 – 3 of 3

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De Lellis-Topping type inequalities for f-Laplacians

Guangyue Huang; Fanqi Zeng — 2016

Studia Mathematica

We establish an integral geometric inequality on a closed Riemannian manifold with ∞-Bakry-Émery Ricci curvature bounded from below. We also obtain similar inequalities for Riemannian manifolds with totally geodesic boundary. In particular, our results generalize those of Wu (2014) for the ∞-Bakry-Émery Ricci curvature.

Vanishing theorems for Killing vector fields on complete hypersurfaces in the hyperbolic space

Guangyue Huang; Hongjuan Li — 2016

Colloquium Mathematicae

We study vanishing theorems for Killing vector fields on complete stable hypersurfaces in a hyperbolic space $ℍ^{n + 1} (- 1)$ . We derive vanishing theorems for Killing vector fields with bounded L²-norm in terms of the bottom of the spectrum of the Laplace operator.

Eigenvalue relationships between Laplacians of constant mean curvature hypersurfaces in $𝕊^{n + 1}$

Bingqing Ma; Guangyue Huang — 2013

Communications in Mathematics

For compact hypersurfaces with constant mean curvature in the unit sphere, we give a comparison theorem between eigenvalues of the stability operator and that of the Hodge Laplacian on 1-forms. Furthermore, we also establish a comparison theorem between eigenvalues of the stability operator and that of the rough Laplacian.

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