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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…
A Restricted Chen-Nagano Variational Principle for the Einstein-Hilbert Functional
Sergey Stepanov, Irina Tsyganok
This paper introduces a restricted Chen-Nagano variational principle for the Einstein-Hilbert functional on compact Riemannian manifolds. Instead of considering arbitrary symmetric…
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…
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…