76 citations · 234 across the 22 of their papers we have counts for
26 papers
A note on the closed range of on q-convex manifolds
Luca Baracco, Alexander Tumanov
We prove that the tangential Cauchy-Riemann operator has closed range on Levi-pseudoconvex CR manifolds that are embedded in a q-convex complex manifold . Our result generalizes…
Stationary discs and finite jet determination for CR mappings in higher codimension
Alexander Tumanov
We discuss stationary discs for generic CR manifolds and apply them to the problem of finite jet determination for CR mappings. We prove that a CR diffeomorphism of two finitely sm…
Scarcity of periodic orbits in outer billiards
Alexander Tumanov
We give a simple proof of our previous result with V. Zharnitsky that the set of period 4 orbits in planar outer billiard with piecewise smooth convex boundary has empty interior,…
Pseudoholomorphic discs and symplectic structures in Hilbert space
Alexandre Sukhov, Alexander Tumanov
We develop the theory of -holomorphic discs in Hilbert spaces with almost complex structures. As an aplication, we prove a version of Gromov's symplectic non-squeezing theorem f…
Symplectic non-squeezing in Hilbert space and discrete Schrödinger equations
Alexandre Sukhov, Alexander Tumanov
We prove a generalization of Gromov's symplectic non-squeezing theorem for the case of Hilbert spaces. Our approach is based on filling almost complex Hilbert spaces by complex dis…
Commutators of singular integrals, the Bergman projection, and boundary regularity of elliptic equations in the plane
Alexander Tumanov
We obtain estimates of commutators of singular integral operators in Lipschitz spaces and apply the results to boundary regularity of elliptic equations in the plane. We obtain an…