Related papers: Holomorphic evolution: metamorphosis of the Loewne…

In this paper we study transversely holomorphic foliations of complex codimension one with some hypothesis on the transverse structure.

Holomorphic manifolds over Cayley-Dickson algebras are defined and their embeddings and immersions are studied.

We study the evolution equations for a regularized version of Dirac-geodesics, which are the one-dimensional version of Dirac-harmonic maps. We show that for the regularization being sufficiently large, the evolution equations subconverge…

This is a survey of recent and classical results concerning various types of homogeneity, such as n-homogeneity, discrete homogeneity, and countable dense homogeneity. Some new results are also presented, and several problems are posed.

Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscosity and heat transfer is taken into account. Exact solutions…

This survey on flexible Weinstein manifolds is, essentially, an extract from our recent joint book.

Recently, we proposed a general evolution equation for single quadrilateral Wilson loop on the light-cone. In present work, we study the energy evolution of a combination of two such loops that partially overlap or have a self-intersection.…

Holomorphic (nondegenerate) mappings between complex manifolds of the same dimension are of special interest. For example, they appear as coverings of complex manifolds. At the same time they have very strong "extra" extension properties in…

We establish new results on weighted $L^2$ extension of holomorphic top forms with values in a holomorphic line bundle, from a smooth hypersurface cut out by a holomorphic function. The weights we use are determined by certain functions…

This paper surveys recent results on classifying partially hyperbolic diffeomorphisms. This includes the construction of branching foliations and leaf conjugacies on three-dimensional manifolds with solvable fundamental group.…

In this paper, we give a complete topological, as well as geometrical classification of closed 3-dimensional Lorentz manifolds admitting a noncompact isometry group.

Given a nonlinear evolution equation in (1+n) dimensions, which has spatially extended traveling wave solutions, it can be extended into a system of two coupled equations, one of which generates the original traveling waves, and the other…

We derive here some mathematical properties of the Weertman equation and show it is the limit of an evolution equation. The Weertman equation is a semilinear integrodifferential equation involving a fractional Laplacian. In addition to this…

Survey article on the geometry of spherical varieties. Invited survey for Transformation Groups.

The possible ways to describe the states of a system of many hard spheres are considered, in particular by means of functions describing correlations of states. It is stated an approach to the description of the evolution based on the…

We study deformations of complex projective varieties that are homotopically or homologically trivial. We formulate several conjectures and give some examples and partial answers.

We investigate a system of geometric evolution equations describing a curvature and torsion driven motion of a family of 3D curves in the normal and binormal directions. We explore the direct Lagrangian approach for treating the geometric…

This paper introduces a notion of decompositions of integral varifolds into countably many integral varifolds, and the existence of such decomposition of integral varifolds whose first variation is representable by integration is…

In this paper, we define a new bigraded L-homology on finite simplicial complexes and prove that L-homology is a homeomorphism invariant of polyhedra.

Complete cosmic evolution is a popular model in cosmology. But the possibility of other different cosmic evolution model can not be negated. The nonsingular bouncing scenario models are now found in literature. This work is a representation…