# Shi-type estimates and finite time singularities of flows of G$_2$ structures

## TL;DR

This paper extends Shi-type estimates to broader G2 structure flows, proves a non-collapsing theorem, and investigates finite time singularities in these geometric flows.

## Contribution

It introduces generalized Shi-type estimates and a non-collapsing theorem for G2 flows, advancing understanding of singularity formation in these geometric evolutions.

## Key findings

- Extended Shi-type estimates to modified Laplacian co-flow.
- Proved a $$-non-collapsing theorem for G2 flows.
- Analyzed finite time singularities in G2 structure flows.

## Abstract

In this paper, we extend Lotay-Wei's Shi-type estimate from Laplacian flow to more general flows of G$_2$ structures including the modified Laplacian co-flow. Then we prove a version of $\kappa$-non-collapsing theorem. We will use both of them to study finite time singularities of general flows of G$_2$ structures.