25 citations · 80 across the 14 of their papers we have counts for
16 papers
Steady flows of ideal incompressible fluid
Vladimir Yu. Rovenski, Vladimir A. Sharafutdinov
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the…
Ray transform on Sobolev spaces of symmetric tensor fields, I: Higher order Reshetnyak formulas
Venky P. Krishnan, Vladimir A. Sharafutdinov
For an integer , we prove the th order Reshetnyak formula for the ray transform of rank symmetric tensor fields on . Certain differential operators $A^{…
Killing tensor fields of third rank on a two-dimensional Riemannian torus
Vladimir A. Sharafutdinov
A rank symmetric tensor field on a Riemannian manifold is called a Killing field if the symmetric part of its covariant derivative is equal to zero. Such a field determines the…
An estimate for the Steklov zeta function of a planar domain derived from a first variation formula
Alexandre Jollivet, Vladimir Sharafutdinov
We consider the Steklov zeta function of a smooth bounded simply connected planar domain R 2 of perimeter 2. We provide a first variation formula for $…
Momentum Ray Transforms, II: Range Characterization In the Schwartz space
Venkateswaran P. Krishnan, Ramesh Manna, Suman Kumar Sahoo +1
The momentum ray transform integrates a rank symmetric tensor field over lines of with the weight : $ (I^k\!f)(x,ξ)=\int_{-\infty}^\infty t^kłf(x+tξ),ξ^…
Application of geometric symbol calculus to computing heat invariants
Vladimir Sharafutdinov
The problem of evaluating heat invariants can be computerized. Geometric symbol calculus of pseudodifferential operators is the main tool of such computerization.