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

Gao Chen

doi:10.1093/qmath/hax060

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

Differential Geometry 2019-05-28 v3

Authors: Gao Chen

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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.

Keywords

G$_2$ structure Shi-type estimate Laplacian flow modified Laplacian co-flow finite time singularity $\kappa$-non-collapsing theorem geometric flow

Cite

@article{arxiv.1703.08526,
  title  = {Shi-type estimates and finite time singularities of flows of G$_2$ structures},
  author = {Gao Chen},
  journal= {arXiv preprint arXiv:1703.08526},
  year   = {2019}
}

Comments

The previous version is too short. So it is merged into a new paper

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