Real analyticity of the modified Laplacian coflow

TL;DR

This paper proves that solutions to the modified Laplacian coflow on compact 7-manifolds are real analytic and establishes unique continuation properties, advancing understanding of G2-structure flows.

Contribution

It improves existing estimates for the flow and demonstrates real analyticity, answering a previously posed open question.

Findings

Enhanced Shi-type estimate for the flow

Proof of real analyticity of solutions

Unique continuation results for the flow

Abstract

Let (M,\psi(t))_{t\in[0, T]} be a solution of the modified Laplacian coflow (1.3) with coclosed G_{2}-structures on a compact 7-dimensional M. We improve Chen's Shi-type estimate [5] for this flow, and then show that (M,\psi(t),g_{\psi}(t)) is real analytic, where g_{\psi}(t) is the associate Riemannian metric to \psi(t), which answers a question proposed by Grigorian in [13]. Consequently, we obtain the unique-continuation results for this flow.