Related papers: Functionals on the space of almost complex stuctur…

This paper presents a rigidity property of the exceptional locus of some kind of small birational contractions. An application in the context of geometric transitions and Calabi-Yau threefolds moduli space is then given, with some physical…

We identify a set of "energy" functionals on the space of metrics in a given Kaehler class on a Calabi-Yau manifold, which are bounded below and minimized uniquely on the Ricci-flat metric in that class. Using these functionals, we recast…

We study the general form of isomorphisms on the algebra of compactly supported complex-valued continuous functions defined on a locally compact Hausdorff space (the proof of which works for the algebra of $C^k-$differentiable functions on…

We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…

We deal with a family of functionals depending on curvatures and we prove for them compactness and semicontinuity properties in the class of closed and bounded sets which satisfy a uniform exterior and interior sphere condition. We apply…

Using the set of functionally open finite covers of completely regular spaces in the paper are constructed Cech type functional homology functor

Let (M, F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian metrics, and consider continuous functions on M that are harmonic along the leaves of F . If every such function is constant on leaves we…

For a compact manifold $M$ of $\dim M =n\geq 4$, we study two conformal invariants of a conformal class $C$ on $M$. These are the Yamabe constant $Y_C(M)$ and the $L^{\frac{n}{2}}$-norm $W_C(M)$ of the Weyl curvature. We prove that for any…

In this note, we will present global equisingular approximations of quasi-plurisubharmonic functions with stable analytic pluripolar sets on compact complex manifolds.

Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…

We study tightness properties and selective versions of separability in bitopological function spaces endowed with set-open topologies.

We describe the supports of a class of real-valued maps on $C*(X)$ introduced by Radul. Using this description, a characterization of compact-valued retracts of a given space in terms of functional extenders is obtained. For example, if…

The objet of this paper is the study of variations of a functional whose integrant is the $\sigma_u$-curvature of closed submanifolds of arbitrary codimension in Riemannian manifolds.

We prove a version of the variational Euler-Lagrange equations valid for functionals defined on Fr\'echet manifolds, such as the spaces of sections of differentiable vector bundles appearing in various physical theories.

These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.

We construct a family of canonical connections and surrounding basic theory for almost complex manifolds that are equipped with an affine connection. This framework provides a uniform approach to treating a range of geometries. In…

Based on a well known Sh.-T. Yau theorem we obtain that the real part of a holomorphic function on a K\"{a}hler manifold with the Ricci curvature bounded from below by $-1$ is contractive with respect to the distance on the manifold and the…

We study the continuous solutions of several classical functional equations by using the properties of the spaces of continuous functions which are invariant under some elementary linear trans-formations. Concretely, we use that the sets of…

The interest of mathematicians in metric $f$-manifolds, in particular, almost contact metric manifolds, is motivated by the study of the geometry and dynamics of contact foliations, as well as their applications in physics. Weak metric…

Some results in C_k-theory are obtained with the use of bornologies. We investigate under which conditions the space of the continuous real functions with the compact-open topology is a productively countably tight space, which yields some…