Related papers: An Extension of Mok's Theorem on the Generalized F…

We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.

Given a foliation $\mathcal{F}$ on $X$ and an embedding $X\subseteq Y$, is there a foliation on $Y$ extending $\mathcal{F}$? Using formal methods, we show that this question has an affirmative answer whenever the embedding is sufficiently…

We consider generalizations of the drifted Laplacian and the Bakry-\'Emery-Ricci tensor, and we prove a version of the mean curvature comparison theorem. Consequently, we prove a Myers-type theorem and a generalization of the…

In this paper, we investigate the extent to which the Bump-Hoffstein conjecture could be generalized for central coverings of general linear groups. We provide evidence for such generalized Bump-Hoffstein conjecture by proving some special…

In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two conjectures as possible extensions, and give a…

We derive a generalized Stokes' theorem, valid in any dimension and for arbitrary loops, even if self intersecting or knotted. The generalized theorem does not involve an auxiliary surface, but inherits a higher rank gauge symmetry from the…

We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case…

A generalization of the Fourier-Mukai transform is proposed. The construction is based on analogy with the classical picture of representations of the Heisenberg group.

In this paper we present the statement of the Firoozbakht's conjecture, some of its consequences if it is proved and we show a consequence of Zhang's theorem concerning the Firoozbakht's conjecture.

We propose an extension of a result by Repetowicz et al. about Wick's theorem and its applications: we first show that Wick's theorem can be extended to the uniform distribution on the sphere and then to the whole class of elliptical…

We obtain an extended Reich fixed point theorem for the setting of generalized cone rectangular metric spaces without assuming the normality of the underlying cone. Our work is a generalization of the main result in \cite{AAB} and…

In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.

We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…

A composition of birational maps given by Laurent polynomials need not be given by Laurent polynomials; however, sometimes---quite unexpectedly---it does. We suggest a unified treatment of this phenomenon, which covers a large class of…

We propose generalized Fermat's conjecture in the framework of arithmetic dynamics, and give evidences. The multi-indexed version is added.

This paper is an extension program of the notion of circle of partition developed in our first paper \cite{CoP}. As an application we prove the Erd\H{o}s-Tur\'{a}n additive base conjecture.

In this note, we extend the theories of the canonical bundle formula and adjunction to the case of generalized pairs. As an application, we study a particular case of a conjecture by Prokhorov and Shokurov.

We formulate extensions of Wilking's Jacobi field splitting theorem to uniformly positive sectional curvature and also to positive and nonnegative intermediate Ricci curvatures.

We give an explicit formula for the Hankel transform of a regular sequence in terms of the coefficients of the associated orthogonal polynomials and the sequence itself. We apply this formula to some sequences of combinatorial interest,…

In this paper, we prove the generalized Chen's conjecture for (F,F')-biharmonic map, which is a critical point of the transversal bienergy functional