Related papers: Examples of differentiable mappings into non-local…

We give a description of complex geodesics and we study the structure of stationary discs in some non-convex domains for which complex geodesics are not unique.

We explicitly compute the Dolbeault cohomologies of certain domains in complex space generalizing the classical Hartogs figure. The cohomology groups are non-Hausdorff topological vector spaces, and it is possible to identify the reduced…

We present simple examples of rational maps of the complex projective plane with equal first and second dynamical degrees and no invariant foliation.

In this brief note, we provide an example of non complete locally convex space $E$ with a $\sigma(E, E^*)$ closed bounded subset $C\subset E$, which is not $\sigma(E, E^*)$-compact, even if every $\varphi\in E^*$ attains its sup over $C$.

In chapter 1 we define period mappings of Hodge-de Rahm type for certain submersive, yet not necessarily locally topologically trivial, morphisms of complex manifolds. Generalizing Griffiths's theory, we interpret the differential of such…

We give an interesting example of a map in $\mathbb{C}^2$ that is tangent to the identity, but that does not have a domain of attraction along any of its characteristic direction. This map has three characteristic directions, two of which…

We apply upper and lower compensated convex transforms, which are `tight' one-sided approximations of a given function, to the extraction of fine geometric singularities from semiconvex/semiconcave functions and DC-functions in…

The present paper mainly presents, for example, explicit classifications of compact smooth manifolds having non-empty boundaries and simple structures where the dimensions are general. Studies of this type is fundamental and important. They…

The Local-to-Global-Principle used in the proof of convexity theorems for momentum maps has been extracted as a statement of pure topology enriched with a structure of convexity. We extend this principle to not necessarily closed maps…

This paper addresses the study and applications of polyhedral duality of locally convex topological vector (LCTV) spaces. We first revisit the classical Rockafellar's proper separation theorem for two convex sets one which is polyhedral and…

We address a linearity problem for differentiable vectors in representations of infinite-dimensional Lie groups on locally convex spaces, which is similar to the linearity problem for the directional derivatives of functions.

We introduce and study the notion of a locally proper map between topological spaces. We show that fundamental constructions of sheaf theory, more precisely proper base change, projection formula, and Verdier duality, can be extended from…

Let $E$ be a locally convex space, $U\subseteq\mathbb{R}^n$ as well as $V\subseteq\mathbb{R}^m$ be open and $k,l\in\mathbb{N}_0\cup\left\{\infty\right\}$. Locally convex spaces $C^{k,l}(U\times V,E)$ of functions with different degrees of…

Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…

We give an explicit verifiable characterization of weakly pseudoconvex but locally nonconvexifiable hypersurfaces of finite type in dimension two. It is expressed in terms of a generalized model, which captures local geometry of the…

We present here "the" cartesian closed theory for real analytic mappings. It is based on the concept of real analytic curves in locally convex vector spaces. A mapping is real analytic, if it maps smooth curves to smooth curves and real…

For locally convex vector spaces (l.c.v.s.) $E$ and $F$ and for linear and continuous operator $T: E \rightarrow F$ and for an absolutely convex neighborhood $V$ of zero in $F$, a bounded subset $B$ of $E$ is said to be $T$-V-dentable…

In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie…

In this paper, we consider abstract nonautonomous difference inclusions in locally convex spaces with integer order differences. We particularly analyze the existence and uniqueness of almost periodic type solutions to abstract…

We construct holomorphic maps with a Siegel disk whose boundary is not locally connected (and is an indecomposable continuum), yet compactly contained in the domain of definition of the map. Our examples are injective and defined on a…