4 papers
Quantitative Rigidity Using Colding's Monotonicity Formulas for Ricci Curvature
Christine Breiner, Jiewon Park
In \cite{Colding}, Colding proved monotonicity formulas for the Green function on manifolds with nonnegative Ricci curvature. Inspired by the sharp estimates relating the pinching…
Rigidity of the gradient estimate for Einstein manifolds
Sanghoon Lee, Jiewon Park
We study the rigidity of Ricci-flat manifolds with quadratic curvature decay under conditions on the Green function. We show that if the gradient of the Green function is uniformly…
Quantitative estimates for the relative isoperimetric problem and its gradient flow outside convex bodies in the plane
Elena Mäder-Baumdicker, Robin Neumayer, Jiewon Park +1
We prove three related quantitative results for the relative isoperimetric problem outside a convex body in the plane: (1) Åojasiewicz estimates and quantitative rigidity for…
Geometric medians on product manifolds
Jiewon Park, Kisung You
Product manifolds arise when heterogeneous geometric variables are jointly observed. While the Fréchet mean on Riemannian manifolds separates cleanly across factors, the canonical…