6 papers · 1 filter
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 nonnegative Ricci curvature, which was extended to positive Ricci curvature by Manea recently…
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 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…
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…
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…