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The aim of this paper is to present a simple way to generate proper monomial rational maps between generalized balls and via the relations between generalized balls and bounded symmetric domains of type I, we suggest new examples of proper…

Correspondences between k-tuples of points are key in multiple view geometry and motion analysis. Regular transformations are posed by homographies between two projective planes that serves as structural models for images. Such…

We analyze geometrical structures necessary to represent bulk and surface interactions of standard and substructural nature in complex bodies. Our attention is mainly focused on the influence of diffuse interfaces on sharp discontinuity…

The existence of closed hypersurfaces of prescribed curvature in globally hyperbolic Lorentzian manifolds is proved provided there are barriers.

We obtain conditions on the Lee form under which a holomorphic map between almost Hermitian manifolds is a harmonic map or morphism. Then we discuss under what conditions (i) the image of a holomorphic map from a cosymplectic manifold is…

We describe a part of the recent developments in the theory of separately holomorphic mappings between complex analytic spaces. Our description focuses on works using the technique of holomorphic discs.

We establish a characterization of the extraordinary dimension of perfect maps between metrizable spaces.

We prove that for any complex manifold X, the set of all holomorphic maps from the unit disc to X whose images are everywhere dense in X forms a dense subset in the space of all holomorphic maps from the disc to X. We show by an example…

We consider various equivalence relations on the set of homotopy classes of curves on a hyperbolic surface based on topological, algebraic, and geometric structures. The purpose of this work is to determine the relationship between these…

We prove that proper pseudo-holomorphic maps between strictly pseudoconvex regions in almost complex manifolds extend to the boundary. The key point is that the Jacobian is far from zero near the boundary, and the proof is mainly based on…

In this paper we define a numerical shape invariant of a continuous map called shape dimension of a map, which generalizes the shape dimension of a topological space. Some basic properties and applications of this invariant are given. The…

We discuss different applications and potentials of reciprocal bianisotropic metasurfaces including uniform and gradient metasurfaces, in particular, with anisotropic, chiral, and omega properties. Based on an analytic analysis, we discuss…

Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…

We construct (infinitely many) examples in all dimensions of contactomorphisms of closed overtwisted contact manifolds that are smoothly isotopic but not contact-isotopic to the identity.

An orientation preserving diffeomorphism over a surface embedded in a 4-manifold is called extendable, if this diffeomorphism is a restriction of an orientation preserving diffeomorphism on this 4-manifold. In this paper, we investigate…

We derive a numerical criterion for J-holomorphic curves in 4-dimensional symplectic cobordisms to achieve transversality without any genericity assumption. This generalizes results of Hofer-Lizan-Sikorav and Ivashkovich-Shevchishin to…

In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…

In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their orientation awareness. More specifically, we…

We prove a result on the structure of finite proper holomorphic mappings between complex manifolds that are products of hyperbolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert…

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…