Related papers: Regularity of CR-mappings between Fuchsian type hy…
We prove analogues of several well-known results concerning rational morphisms between quadrics for the class of so-called quasilinear $p$-hypersurfaces. These hypersurfaces are nowhere smooth over the base field, so many of the geometric…
We prove and organize some results on the normal forms of Hermitian operators composed with the Veronese map. We apply this general framework to prove two specific theorems in CR geometry. First, extending a theorem of Faran, we classify…
We introduced a new coordinate-free approach to study the Cauchy-Riemann (CR) maps between the real hyperquadrics in the complex projective space. The central theme is based on a notion of orthogonality on the projective space induced by…
We prove the algebraicity of smooth $CR$-mappings between algebraic Cauchy--Riemann manifolds. A generalization of separate algebraicity principle is established.
In Cayley graphs on the additive group of a small vector space over GF$(q)$, $q=2,3$, we look for completely regular (CR) codes whose parameters are new in Hamming graphs over the same field. The existence of a CR code in such Cayley graph…
We describe a normal form for a smooth intersection of two quadrics in even-dimensional projective space over an arbitrary field of characteristic 2. We use this to obtain a description of the automorphism group of such a variety. As an…
We develop the regularity theory of viscosity solutions to transmission problems for fully nonlinear second order uniformly elliptic equations. Our results give a complete theory of existence, uniqueness, comparison principle, and…
We first show that the union of a projective curve with one of its extremal secant lines satisfies the linear general position principle for hyperplane sections. We use this to give an improved approximation of the Betti numbers of curves…
We study infinite translation surfaces which are Z-covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition…
We study hypersurfaces with fractional mean curvature in N-dimensional Euclidean space. These hypersurfaces are critical points of the fractional perimeter under a volume constraint. We use local inversion arguments to prove existence of…
We consider projection algorithms for solving (nonconvex) feasibility problems in Euclidean spaces. Of special interest are the Method of Alternating Projections (MAP) and the Douglas-Rachford or Averaged Alternating Reflection Algorithm…
The aim of this paper is to give a generalization of the theory equivariant functions, initiated in [17, 4], to arbitrary subgroups of PSL2(R). We show that there is a deep relation between the geometry of these groups and some analytic and…
We classify rational surfaces for which the image of the automorphisms group in the group of linear transformations of the Picard group is the largest possible. This answers a question raised by Arthur Coble in 1928, and can be rephrased in…
In this paper, we study hypersurfaces in $\mathbb{H}^2\times\mathbb{H}^2$. We first classify the hypersurfaces with constant principal curvatures and constant product angle function. Then, we classify homogeneous hypersurfaces and…
In this paper, we give a finiteness result on the diffeomorphism types of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric space. Furthermore, the condition curvature-adapted can be dropped if the symmetric…
In this paper, motivated by the work of Kim and Kolar for the case of pseudoconvex models which are sums of squares of polynomials, we study the Lie algebra of real-analytic infinitesimal $CR$ automorphisms of a model hypersurface $M_0$…
An analytico-geometric reflection principle is established by means of normal deformations of analytic discs.
Let H:(M,p)->(M',p') be a formal mapping between two germs of real-analytic generic submanifolds in C^N with nonvanishing Jacobian. Assuming M to be minimal at p and M' holomorphically nondegenerate at p', we prove the convergence of the…
We compare real and complex dynamics for automorphisms of rational surfaces that are obtained by lifting \chg{some} quadratic birational maps of the plane. In particular, we show how to exploit the existence of an invariant cubic curve to…
In this work, we develop a framework for shape analysis using inconsistent surface mapping. Traditional landmark-based geometric morphometrics methods suffer from the limited degrees of freedom, while most of the more advanced non-rigid…