Author

Jiewon Park

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Preprint Sep 2026

Rigidity and volume pinching for the sharp gradient estimate in positive Ricci curvature

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. We prove almost rigidity of such gradient estimates for positive Ricci curvature. We show that the average of the gradient deficit, namely...

Junyoung Kim, Jiewon Park · 0 citations

Preprint Sep 2026

Weighted volume monotonicity and isoperimetric comparison under a lower Ricci curvature bound

We establish a weighted extension of the Bishop-Gromov volume comparison theorem for complete Riemannian manifolds with Ricci curvature bounded below. Given a point $p$ and positive radial weights $f$ and $h$, we consider the weighted volume of a geodesic ball and a corresponding model weighted volume in the simply con...

Jiewon Park, Keomkyo Seo · 0 citations