Expanding Ricci solitons coming out of weakly PIC1 metric cones

Abstract

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 flow must be an expanding gradient Ricci soliton, and as a consequence, any metric cone at infinity of a complete weakly PIC1 K\"ahler manifold with Euclidean volume growth is biholomorphic to complex Euclidean space in a canonical way.Comment: 21 pages, minor changes, all comments are welcom