Theoretical analysis demonstrates expanding soliton formation in complete weakly PIC1 Ricci flows from metric cones, indicating canonical equivalence to complex Euclidean space.
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.
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Chan et al. (2024) studied this question.
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