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math.DG2025
On critical maps of the horizontal energy functional between Riemannian foliations
Tian Chong, Yuxin Dong, Xin Huang +1
In this paper, we consider critical points of the horizontal energy $E_{\HH}(f)$ for a smooth map between two Riemannian foliations. These critical points are referred to as ho…
math.DG2025
Sobolev Inequality In Manifolds With Lower Quadratic Curvature Decay
Tian Chong, Han Luo, Lingen Lu
By using the ABP method developed by Cabré and Brendle, we establish some Sobolev inequalities for compact domains and submanifolds in a complete Riemannian manifold with lower qua…