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math.DG2019★ 3 cited
Two inequalities for convex equipotential surfaces
Yajun Zhou
We establish two geometric inequalities, respectively, for harmonic functions in exterior Dirichlet problems, and for Green's functions in interior Dirichlet problems, where the bo…
math.DG2019
Some geometric relations for equipotential curves
Yajun Zhou
Let be a harmonic function that solves an exterior Dirichlet problem. If all the level sets of $U(\boldsymbol r),\boldsymbol…
math.DG2013★ 5 cited
A Simple Formula for Scalar Curvature of Level Sets in Euclidean Spaces
Yajun Zhou
A simple formula is derived for the Ricci scalar curvature of any smooth level set embedded in the Euclidean space , in terms of the grad…