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The Harmonic Variational Principle for the Einstein-Hilbert Functional
Sergey Stepanov, Irina Tsyganok
Let (M,g) be a compact n-dimensional Riemannian manifold, n>2. We introduce a restricted variational principle for the Einstein-Hilbert functional by requiring the admissible metri…
An Inequality Comparing the Dirichlet Energy and the Bienergy of Maps Between Riemannian Manifolds
Sergey Stepanov, Irina Tsyganok
We establish a geometric inequality relating the Dirichlet energy and the bienergy of smooth maps \[ f : (M,g) \to (\overline{M},\overline{g}) \] between Riemanni…
Localized Curvature Domination and Rigidity of Harmonic Maps
Sergey Stepanov
We establish a localized Bochner-type rigidity theorem for harmonic maps between Riemannian manifolds. Let be a harmonic map from a comp…
Extensions and Applications of Stein-Weiss Operators to the Study of Traceless Symmetric Tensors
Sergey Stepanov, Irina Tsyganok
First-order differential operators arising from the representation-theoretic decomposition of the covariant derivative play a central role in Riemannian geometry. In this paper, we…