Related papers: A remark on H1 martingales
An integral polytope is a polytope whose vertices have integer coordinates. A unimodular triangulation of an integral polytope in $\mathbb{R}^d$ is a triangulation in which all simplices are integral with volume $1/d!$. A classic result of…
We define complete stable pairs on a smooth projective variety, and construct their moduli space. These moduli spaces have natural morphisms to the moduli of stable pairs and Quot-schemes. As an example, we show that the moduli of complete…
In this article we explain that several integrable mechanical billiards in the plane are connected via conformal transformations. We first remark that the free billiard in the plane are conformal equivalent to infinitely many billiard…
In this paper we investigate the Margulis-Ruelle inequality for general Riemannian manifolds (possibly noncompact and with boundary) and show that it always holds under integrable condition.
The purpose of this note is to present two elementary, but useful, facts concerning actions on uniformly convex spaces. We demonstrate how each of them can be used in an alternative proof of the triviality of the first $L_p$-cohomology of…
In this paper we introduce the notion of cofrontal mappings, as the dual objects to frontal mappings, and study their basic local and global properties. Cofrontals are very special mappings and far from generic nor stable except for the…
We put in a general framework the situations in which a Riemannian manifold admits a family of compatible complex structures, including hyperkahler metrics and the Spin-rotations of arxiv:1302.2846. We determine the (polystable) holomorphic…
A holomorphic triple over a compact Riemann surface consists of two holomorphic vector bundles and a holomorphic map between them. After fixing the topological types of the bundles and a real parameter, there exist moduli spaces of stable…
We investigate when the tangent bundle of a projective manifold has a non-trivial first order (or positive-dimensional) deformation. This leads to a new conjectural characterization of the complex projective space.
One of the most basic, longstanding open problems in the theory of dynamical systems is whether reachability is decidable for one-dimensional piecewise affine maps with two intervals. In this paper we prove that for injective maps, it is…
A new kind of duality between the deep structures of spacetime and matter is proposed here, considering two partial orders which incorporate causality, extensity, and discreteness. This may have surprising consequences for the emergence of…
In this paper we derive characterizations of boundedness of the subsequences of partial sums with respect to Vilenkin system on the martingale Hardy spaces when $ 0<p<1 $. Moreover, we find necessary and sufficient conditions for the…
Grafakos systematically proved that $A_\infty$ weights have different characterizations for cubes in Euclidean spaces in his classical text book. Very recently, Duoandikoetxea, Mart\'{\i}n-Reyes, Ombrosi and Kosz discussed several…
We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the…
We prove that the martingale dimensions for canonical diffusion processes on a class of self-similar sets including nested fractals are always one. This provides an affirmative answer to the conjecture of S. Kusuoka [Publ. Res. Inst. Math.…
We present an example of an integrable Hamiltonian system with scalar potential in the three-dimensional Euclidean space whose integrals of motion are quadratic polynomials in the momenta, yet its Hamilton-Jacobi / Schrodinger equation…
The question of the existence of Universal homotopy commutative and homotopy associative H-spaces (called Abelian H-spaces) is studied. Such a space T(X) would prolong a map from X into an Abelian H-space to a unique H-map from T into X.…
A moving parallel frame method is applied to geometric non-stretching curve flows in the Hermitian symmetric space Sp(n)/U(n) to derive new integrable systems with unitary invariance. These systems consist of a bi-Hamiltonian modified…
Integrability in string/field theories is known to emerge when considering dynamics in the moduli space of physical theories. This implies that one has to look at the dynamics with respect to unusual time variables like coupling constants…
We analyse supermembrane instantons (fully wrapped supermembranes) by computing the partition function of the three-dimensional supersymmetrical U(N) matrix model under periodic boundary conditions. By mapping the model to a cohomological…