11 papers
Weighted volume monotonicity and isoperimetric comparison under a lower Ricci curvature bound
Jiewon Park, Keomkyo Seo
We establish a weighted extension of the Bishop-Gromov volume comparison theorem for complete Riemannian manifolds with Ricci curvature bounded below. Given a point and positiv…
Rigidity and volume pinching for the sharp gradient estimate in positive Ricci curvature
Junyoung Kim, Jiewon Park
Colding established a sharp gradient estimate for the Green function on manifolds with non-negative Ricci curvature, which was extended to positive Ricci curvature by Manea recentl…
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) Łojasiewicz estimates and quantitative rigidity for c…
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…
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…
Monotonicity formulas and Hessian of the Green function
Jiewon Park
Based on an assumption on the Hessian of the Green function, we derive some monotonicity formulas on nonparabolic manifolds. This assumption is satisfied on manifolds that meet cer…
A Matrix Li-Yau-Hamilton estimate for the Green function on Kähler manifolds
Jiewon Park
In this paper we prove a matrix Li-Yau-Hamilton inequality for the Green function on complete Kähler manifolds with nonnegative holomorphic bisectional curvature. This estimate can…
Canonical identification at infinity for Ricci-flat manifolds
Jiewon Park
We give a natural way to identify between two scales, potentially arbitrarily far apart, in a non-compact Ricci-flat manifold with Euclidean volume growth when a tangent cone at in…
A Compactness Theorem for Rotationally Symmetric Riemannian Manifolds with Positive Scalar Curvature
Jiewon Park, Wenchuan Tian, Changliang Wang
Gromov and Sormani conjectured that sequences of compact Riemannian manifolds with nonnegative scalar curvature and area of minimal surfaces bounded below should have subsequences…
Matrix Inequality for the Laplace Equation
Jiewon Park
Since Li and Yau obtained the gradient estimate for the heat equation, related estimates have been extensively studied. With additional curvature assumptions, matrix estimates that…