Related papers: Generalized gyrovector spaces revisited
In this paper, we prove a transversality theorem for the moduli space of perturbed special Lagrangian submanifolds in a 6-dimensional manifold equipped with a generalization of a Calabi-Yau structure. These perturbed special Lagrangian…
We present some results and conjectures on a generalization to the noncommutative setup of the Brouwer fixed-point theorem from the Borsuk-Ulam theorem perspective.
This paper states and proves a generalization of the well-known Desargues involution theorem from plane projective geometry.
The weighted triangulation algebras associated to triangulation quivers and their socle deformations were recently introduced and studied in [15]-[20] and [2]. These algebras, based on surface triangulations and originated from the theory…
We give a combinatorial proof, using the hyperbolicity of the curve graphs, of the bounded geodesic image theorem of Masur and Minsky. Recently it has been shown that curve graphs are uniformly hyperbolic, thus a universal bound can be…
We prove a generalization of Gowers' theorem for $\mathrm{FIN}_{k}$ where, instead of the single tetris operation $T:\mathrm{FIN}_{k}\rightarrow \mathrm{FIN}_{k-1}$, one considers all maps from $\mathrm{FIN}_{k}$ to $\mathrm{FIN}_{j}$ for…
Let $(\Omega,\mu)$ be a $\sigma$-finite measure space. Given a Banach space $X$, let the symbol $S(X)$ stand for the unit sphere of $X$. We prove that the space $L^{\infty} (\Omega,\mu)$ of all complex-valued measurable essentially bounded…
We discuss some variants of cone theorem for movable curves in any codimensions.
We prove a general form of Green Formula and Cauchy Integral Theorem for arbitrary closed rectifiable curves in the plane.
This note is intended to reformulate the Dixmier-Malliavin theorem about smooth group representations in the language of bornological vector spaces, instead of topological vector spaces. This language turns out to allow a more general…
This paper studies linear generalised complex structures over vector bundles, as a generalised geometry version of holomorphic vector bundles. In an adapted linear splitting, a linear generalised complex structure on a vector bundle $E\to…
We investigate the embedding variable approach to geometrodynamics advocated in work by Isham, Kucha\v{r} and Unruh for a general class of coordinate conditions that mirror the Isham-Kucha\v{r} Gaussian condition but allow for arbitrary…
The aim of this paper is to present necessary and sufficient conditions for generalized H\"{o}lder's inequality on generalized Morrey spaces. We also obtain similar results on weak Morrey spaces and on generalized weak Morrey spaces. The…
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…
We will present a new proof of the Gromoll-Grove diameter rigidity theorem.
We prove some Bernstein theorems for entire space-like submanifolds in pseudo-Euclidean spaces and, as a corollary, we obtain a new proof of the Calabi-Pogorelov theorem on global solutions of Monge-Ampere equations.
In this paper, we propose another characterization of the generalized mirror transformation on the quantum cohomology rings of general type projective hypersurfaces. This characterics is useful for explicit determination of the form of the…
In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.
In his celebrated paper "Generic projections", John Mather has given a striking transversality theorem and its applications on generic projections. On the other hand, in this paper, two transversality theorems on generic linearly perturbed…
In this paper, we explicitly derive the generalized mirror transformation of quantum cohomology of general type projective hypersurfaces, proposed in our previous article, as an effect of coordinate change of the virtual Gauss-Manin system.