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math.DG2021★ 1 cited
Existence of curves with constant geodesic curvature in a Riemannian 2-sphere
Da Rong Cheng, Xin Zhou
We prove the existence of immersed closed curves of constant geodesic curvature in an arbitrary Riemannian 2-sphere for almost every prescribed curvature. To achieve this, we devel…
math.DG2020
Stable solutions to the abelian Yang--Mills--Higgs equations on and
Da Rong Cheng
We show under natural assumptions that stable solutions to the abelian Yang--Mills--Higgs equations on Hermitian line bundles over the round -sphere actually satisfy the vortex…
math.DG2015
A compactness result for energy-minimizing harmonic maps with rough domain metric
Da Rong Cheng
In 1996, Shi generalized the epsilon-regularity theorem of Schoen and Uhlenbeck to energy-minimizing harmonic maps from a domain equipped with a bounded measurable Riemannian metri…