8 citations · 14 across the 8 of their papers we have counts for
9 papers · 1 filter
Energy convexity and uniformity of the -surface flow in with Dirichlet boundary condition
Da Rong Cheng, Longzhi Lin, Xin Zhou
We prove that the energy functional associated with surfaces of prescribed mean curvature in exhibits a convexity property when restricted to maps from the unit -…
Existence of classical minimal surfaces in and -manifolds
Da Rong Cheng, Xin Zhou
We prove that every closed Riemannian or -manifold contains a branched immersed closed minimal surface. That is, there exists a non-constant weakly conformal harmonic ma…
Holomorphicity of parabolic stable minimal surfaces of high codimension
Da Rong Cheng, Spiro Karigiannis, Jesse Madnick
A classical theorem of Micallef says that if is a stable minimal immersion of an oriented -dimensional complete Riemannian manifold (that is p…
Yang-Mills-Higgs functional with Higgs self-interaction on -manifolds
Da Rong Cheng, Daniel Fadel, Luiz Lara
Given a constant , for any parameter we study critical points of the Yang--Mills--Higgs energy \[ \mathcal{Y}_{\varepsilon}(\nabla,Φ) = \int_M \left(\varepsilo…
Existence of constant mean curvature disks in with capillary boundary condition
Da Rong Cheng
We extend Struwe's result (Acta Math., 1988) on the existence of free boundary constant mean curvature disks to almost every prescribed boundary contact angle in . Specific…
A variational characterization of calibrated submanifolds
Da Rong Cheng, Spiro Karigiannis, Jesse Madnick
Let be a fixed compact oriented embedded submanifold of a manifold . Consider the volume as a function…
Existence of free boundary disks with constant mean curvature in
Da Rong Cheng
Given a surface in diffeomorphic to , Struwe (Acta Math., 1988) proved that for almost every below the mean curvature of the smallest sphere enclosing $…
Existence of constant mean curvature 2-spheres in Riemannian 3-spheres
Da Rong Cheng, Xin Zhou
We prove the existence of branched immersed constant mean curvature 2-spheres in an arbitrary Riemannian 3-sphere for almost every prescribed mean curvature, and moreover for all p…
Bubble Tree Convergence of Conformally Cross Product Preserving Maps
Da Rong Cheng, Spiro Karigiannis, Jesse Madnick
We study a class of weakly conformal -harmonic maps, called associative Smith maps, from -manifolds into -manifolds that parametrize associative -folds in Riemannian $7…