相关论文: On extremal function of a modulus of a foliation

We study the existence of first integral for holomorphic foliations in different scenarios and under different conditions, for instance germ of foliations given by vector fields and having a formal first integral or infinitely many…

As the loop space of a Riemannian manifold is infinite-dimensional, it is a non-trivial problem to make sense of the "top degree component" of a differential form on it. In this paper, we show that a formula from finite dimensions…

We obtained that any 2-form and any smooth function on 2-manifolds with boundary can be realized as the curvature form and the gaussian curvature function of some Riemmanian metric, respectively.

We present examples of foliations with infinite dimensional basic symplectic and com- plex cohomologies, along with a general sufficient condition for such phenomena. This puts re- strictions on possible generalizations of several…

In this manuscript we present how to collapse a manifold equipped with a closed flat regular Riemannian foliation with leaves of positive dimension, while keeping the sectional curvature uniformly bounded from above and below. From this…

We study the geometry of a codimension-one foliation with a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as the Riemannian metric varies along the leaves of the foliation.…

Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail. In particular, the homology groups and the homotopy type…

In this paper, we study modularity of several functions which naturally arose in a recent paper of Lau and Zhou on open Gromov-Witten potentials of elliptic orbifolds. They derived a number of examples of indefinite theta functions, and we…

We investigate the existence and uniqueness of solutions for second-order semi-linear partial differential equations defined on a Riemannian manifold $M$. By combining differential geometry and analysis techniques, we establish the…

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…

The present article is a study of germs of regular foliations transverse to an embedded strongly exceptional submanifold of a complex manifold. Cohomological conditions are given on this embedding for the existence of these foliations and…

We consider two types of fractional integral moduli of smoothness, which are widely used in theory of functions and approximation theory. In particular, we obtain new equivalences between these moduli of smoothness and the classical moduli…

We construct spectral triples in a sense of noncommutative differential geometry, associated with a Riemannian foliation on a compact manifold, and describe its dimension spectrum.

Elementary facts and observations on the cone of supermodular set functions are recalled. The manuscript deals with such operations with set functions which preserve supermodularity and the emphasis is put on those such operations which…

We prove a Slice Theorem around closed leaves in a singular Riemannian foliation, and we use it to study the $C^\infty$-algebra of smooth basic functions, generalizing to the inhomogeneous setting a number of results by G.~Schwarz. In…

Adaptive estimation of linear functionals over a collection of parameter spaces is considered. A between-class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability over two…

We establish plurisubharmonicity of envelopes of certain classical disc functionals on locally irreducible complex spaces, thereby generalizing the corresponding results for complex manifolds. We also find new formulae expressing the…

We show that on every manifold, every conformal class of semi-Riemannian metrics contains a metric $g$ such that each $k$-th-order covariant derivative of the Riemann tensor of $g$ has bounded absolute value $a_k$. This result is new also…

This article provides a brief discussion of the functional of super Riemann surfaces from the point of view of classical (i.e. not "super-) differential geometry. The discussion is based on symmetry considerations and aims to clarify the…

In this paper, we establish a number of results about the topology of the leaves of a closed singular Riemannian foliation $(M,\fol)$. If $M$ is simply connected, we prove that the leaves are finitely covered by nilpotent spaces, and…