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Infinite-dimensional manifolds modelled on arbitrary Hilbert spaces of functions are considered. It is shown that changes in model rather than changes of charts within the same model make coordinate formalisms on finite and…

The convenient setting for smooth mappings, holomorphic mappings, and real analytic mappings in infinite dimension is sketched. Infinite dimensional manifolds are discussed with special emphasis on smooth partitions of unity and tangent…

In the recent work [Metrically round and sleek metric spaces, \emph{The Journal of Analysis} (2022), pp 1--17], the authors proved some results on metrically round and sleek linear metric spaces and metric spaces. In continuation, the…

In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…

We describe the canonical correspondence between set of all finite metric spaces and set of special symmetric convex polytopes, and formulate the problem about classification of the metric spaces in terms of combinatorial structure of those…

This article presents a survey of some recent results in the theory of spatial graphs. In particular, we highlight results related to intrinsic knotting and linking and results about symmetries of spatial graphs. In both cases we consider…

In this survey, we give an introduction to nearly K\"ahler geometry, and list some results on submanifolds of these spaces. This survey tries by no means to be complete.

We prove some extension results for holomorphic mappings with values in complex Hilbert manifolds

We get sharp degree bound for generic smoothness and connectedness of the space of conics in low degree complete intersections which generalizes the old work about Fano scheme of lines on Hypersurfaces.

We consider biharmonic submanifolds in both generalized complex and Sasakian space forms. After giving the biharmonicity conditions for submanifolds in these spaces, we study different particular cases for which we obtain curvature…

Let X be a compact (resp. compact and nonsingular) real algebraic variety and let Y be a homogeneous space for some linear real algebraic group. We prove that a continuous (resp. C^infinity) map f:X-->Y can be approximated by regular maps…

We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…

We construct equivariant harmonic maps between cohomogeneity one manifolds.

We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.

Several characterizations of complex ellipsoids among convex bodies in Cn, in terms of their sections and projections are proved. Characterizing complex symmetry in similar terms is an important tool.

We study some special almost complex structures on strictly pseudoconvex domains. They appear naturally as limits under a nonisotroping scaling procedure and play a role of model objects in the geometry of almost complex manifolds with…

We give a short proof of the convergence to the boundary of Riemann maps on varying domains. Our proof provides a uniform approach to several ad-hoc constructions that have recently appeared in the literature.

We study proper holomorphic mappings between strictly pseudoconvex domains with low boundary regularity.

In this informal expository note, we quickly introduce and survey compactifications of strata of holomorphic 1-forms on Riemann surfaces, i.e. spaces of translation surfaces. In the last decade, several of these have been constructed,…

Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion…