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riemannian geometry – Infimum of the Dirichlet power and deformation of metrics Answer

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riemannian geometry – Infimum of the Dirichlet power and deformation of metrics

Consider the Dirichlet power $E(phi; g,h)=frac{1}{2}int_M|dphi|^2$ of a map $phi:(M,g)to(N,h)$ between Riemannian manifolds, the place we occupy $M$ and $N$ are compact. Given a path $g(t)$ of Riemannian metrics on $M$, deem the duty commence{equation}t mapstoinf_{phi}E(phi; g(t),h),aim{equation} the place the infimum is taken over a hard and fast homotopy class of maps $Mto N$. I used to be questioning whether or not there’s any regularity outcome for this duty, or if there’s any good reference on this theme?

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