In this paper, we obtain the existence of Dirichlet problem for VT harmonic map from compact Riemannian manifold with or without boundary into compact manifold via the heat flow method. We also obtain the existence of V T geodesics uncer certain conditions on T.
Decompositions of the space of Riemannian metrics on a compact manifold with boundary
On the $σ_2$-curvature and volume of compact manifolds
Landau levels on a compact manifold
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