8 papers · 1 filter
Gromov-Hausdorff limits of immortal Kähler-Ricci flows
Man-Chun Lee, Valentino Tosatti, Junsheng Zhang
We show that the normalized Kähler-Ricci flow on a compact Kähler manifold with semiample canonical bundle converges in the Gromov-Hausdorff topology to the metric completion of th…
Higher-dimensional flying wing Steady Ricci Solitons
Pak-Yeung Chan, Yi Lai, Man-Chun Lee
For any , we construct an -parameter family of steady gradient Ricci solitons with non-negative curvature operator and prescribed by the eigenvalues of Ricci tensor…
Local mollification of metrics with small curvature concentration
Man-Chun Lee, Tang-Kai Lee
In this work, we establish a local smoothing result on metrics with small curvature concentration with respect to Sobolev constants and volume growth. In contrast with all previous…
Gap Theorem on locally conformally flat manifold
Ming Hsiao, Man-Chun Lee
In this work, we study a gap phenomenon in locally conformally flat Riemannian manifolds with non-negative Ricci curvature. We construct complete solutions to the Yamabe flow that…
On the weakly conical expanding gradient Ricci solitons
Pak-Yeung Chan, Man-Chun Lee
In this work, we construct several sequences of metrics on sphere with different limiting behaviors. By combining with the work of Deruelle, we use it and the localized maximum pri…
Expanding Ricci solitons coming out of weakly PIC1 metric cones
Pak-Yeung Chan, Man-Chun Lee, Luke T. Peachey
Motivated by recent work of Deruelle-Schulze-Simon, we study complete weakly PIC1 Ricci flows with Euclidean volume growth coming out of metric cones. We show that such a Ricci flo…