Monotonicity formula for heat flow for Yang-Mills-Higgs equations

Research Report MRR98-008

Monotonicity formula for heat flow for Yang-Mills-Higgs equations

Min-Chun Hong

Abstract: For a parameter $\lambda >0$ , we consider heat flow for the Yang-Mills-Higgs equations in a vector bundle over a compact m-dimensional Riemannian manifold and establish a uniform monotonicity formula in $\lambda$ for these flow. Our monotonicity formula unify those for heat flow of both harmonic maps and Yang-Mills equations. Moreover, we also prove the global existence of the smooth solution to the heat flow for Yang-Mills-Higgs equations for each fixed parameter $\lambda >0$ in the case of m=3.

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