Weakly PIC1 manifolds with maximal volume growth

TL;DR

This paper uses Ricci flow techniques to prove that complete PIC1 manifolds with maximal volume growth are diffeomorphic to Euclidean space, providing new curvature estimates and pseudolocality results.

Contribution

It introduces local curvature estimates and pseudolocality results for PIC1 manifolds, establishing their topological equivalence to Euclidean space under maximal volume growth.

Findings

PIC1 manifolds with maximal volume growth are diffeomorphic to ℝ^n

Established local curvature lower bounds during Ricci flow

Derived pseudolocality results related to PIC1 condition

Abstract

In this article we use Ricci flow to show that complete PIC1 manifolds with maximal volume growth are diffeomorphic to $\mathbb{R}^n$. One of the key ingredients is local estimates of curvature lower bounds on an initial time interval of the Ricci flow. As another application of these estimates we obtain pseudolocality type results related to the PIC1 condition.