56 citations · 321 across the 19 of their papers we have counts for
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Hölder regularity of the equation on the polydisc
Yu Jun Loo, Alexander Tumanov
In this note, we show the existence of a solution operator to the equation in the polydisc that preserves Hölder regularity. This solution operator is constructed us…
Infinitesimal automorphisms of quadrics and second jet determination for CR mappings
Alexander Tumanov
We consider a problem whether a CR mapping of a generic manifold in complex space is uniquely determined by its finite jet at a point, which is referred to as finite jet determinat…
Hartogs figure and symplectic non-squeezing
A. Sukhov, A. Tumanov
We solve a problem on filling by Levi-flat hypersurfaces for a class of totally real 2-tori in a real 4-manifold with an almost complex structure tamed by an exact symplectic form.…
Deformations and transversality of pseudo-holomorphic discs
A. Sukhov, A. Tumanov
We prove analogs of Thom's transversality theorem and Whitney's theorem on immersions for pseudo-holomorphic discs. We also prove that pseudo-holomorphic discs form a manifold.
Regularization of almost complex structures and and gluing holomorphic discs to tori
A. Sukhov, A. Tumanov
We prove a result on removing singularities of almost complex structures pulled back by a non-diffeomorphic map. As an application we prove the existence of global J-holomorphic di…