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- W3104744552 abstract "Given a $7$-dimensional compact Riemannian manifold $left( M,gright) $ that admits $G_{2}$-structure, all the $G_{2}$-structures that are compatible with the metric $g$ are parametrized by unit sections of an octonion bundle over $M$. We define a natural energy functional on unit octonion sections and consider its associated heat flow. The critical points of this functional and flow precisely correspond to $G_{2}$-structures with divergence-free torsion. In this paper, we first derive estimates for derivatives of $Vleft( tright) $ along the flow and prove that the flow exists as long as the torsion remains bounded. We also prove a monotonicity formula and and an $varepsilon $-regularity result for this flow. Finally, we show that within a metric class of $G_{2}$-structures that contains a torsion-free $G_{2}$-structure, under certain conditions, the flow will converge to a torsion-free $G_{2}$-structure." @default.
- W3104744552 created "2020-11-23" @default.
- W3104744552 creator A5039760920 @default.
- W3104744552 date "2019-09-30" @default.
- W3104744552 modified "2023-10-01" @default.
- W3104744552 title "Estimates and monotonicity for a heat flow of isometric $$G_{2}$$-structures" @default.
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- W3104744552 doi "https://doi.org/10.1007/s00526-019-1630-0" @default.
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