arXiv research

Solves pair trading problem using consumption-investment theory.

Paper extends Kobayashi-Hitchin correspondence to non-Kähler manifolds.

Defines and analyzes the holonomy Lie algebra of geometric lattices.

We study post-Lie algebra structures on pairs of Lie algebras (g,n), and prove existence results for the case that one of the Lie algebras is semisimple. For semisimple g and solvable n we show that there exist no post-Lie algebra structures on (g,n). For semisimple n and certain solvable g we construct canonical post-…

Constructs mirror pairs for solvmanifolds using Lie groups.

The study classifies nilpotent Lie foliations with cohomological obstructions.

For fibered knots, the MQ and Nakanishi indices are equal under certain conditions.

Complex manifold describes solvable Pell-Abel equations with fixed degrees.

Let G be a three-dimensional unimodular Lie group, and let T be a left-invariant symmetric (0, 2)-tensor field on G. We provide the necessary and sufficient conditions on T for the existence of a pair (g, c) consisting of a left-invariant Riemannian metric g and a positive constant c such that Ric(g) = cT, where Ric(g)…

This article concludes the comprehensive study started in [Sz5], where the first non-trivial isospectral pairs of metrics are constructed on balls and spheres. These investigations incorporate 4 different cases since these balls and spheres are considered both on 2-step nilpotent Lie groups and on their solvable extens…

We consider a special family of occupation-time derivatives, namely proportional step options introduced by Linetsky in [Math. Finance, 9, 55--96 (1999)]. We develop new closed-form spectral expansions for pricing such options under a class of nonlinear volatility diffusion processes which includes the constant-elastic…

Extended logarithm for solvable elements in mapping class groups.

Study on solvable Lie groups with specific Weyl connections.

Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ODEs by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries. In fact, under regularity assumptions, any given ODE always admits solvable struc…

Characterizes problems solvable via linear convergence algorithms.

Proves non-solvability of concordance groups using Milnor invariants.

Proves local solvability for $G_2$-structures with Poisson equations.

A Levi-Malcev type decomposition for $2$-step solvable Lie algebras with a complex structure

We exhibit a family of infinite, finitely-presented, nilpotent-by-abelian groups. Each member of this family is a solvable S-arithmetic group that is related to Baumslag-Solitar groups, and everyone of these groups has a quasi-isometry group that is virtually a product of a solvable real Lie group and a solvable p-adic…

Extends confining subset theory to describe hyperbolic actions of solvable groups with higher rank abelianizations.

A {\em solvable} cover of a graph is a regular cover whose covering transformation group is solvable. In this paper, we show that a solvable cover of a graph can be decomposed into layers of abelian covers, and also, a lift of a given automorphism of the base graph of a solvable cover can be decomposed into layers of l…

Let $G$ be a connected Lie group and $Γ\subset G$ a lattice. Connection curves of the homogeneous space $M=G/Γ$ are the orbits of one parameter subgroups of $G$. To $block$ a pair of points $m_1,m_2 \in M$ is to find a finite set $B \subset M\setminus \{m_1, m_2 \}$ such that every connecting curve joining $m_1$ and $m…

Classifies Ricci soliton subgroups in specific Lie groups.

It is shown that a closed solvable subgroup of a connected Lie group is compactly generated. In particular, every discrete solvable subgroup of a connected Lie group is finitely generated. Generalizations to locally compact groups are discussed as far as they carry.

Study on complex curves in hypercomplex nilmanifolds with quaternionic-solvable Lie algebras.

Flat hypercomplex nilmanifolds have a specific solvability property.

Counterexample found for Stein property of certain solvable Lie groups.

We give the classification of solvable and splitting Lie triple system and it turn that, up to isomorphism there exist 7 non isomorphic canonical Lie triple systems and 6 non isomorphic splitting canonical Lie triple systems and find the solvable Lie algebras associated.

Local description of solvable Lie algebras of vector fields.

A compact solvmanifold of completely solvable type, i.e. a compact quotient of a completely solvable Lie group by a lattice, has a Kähler structure if and only if it is a complex torus. We show more in general that a compact solvmanifold $M$ of completely solvable type endowed with an invariant complex structure $J$ ad…

Let $ω_\mathfrak{g}$ be a Lie algebra valued differential $1$-form on a manifold $M$ satisfying the structure equations $d ω_\mathfrak{g} + \frac{1}{2} ω_\mathfrak{g}\wedge ω_\mathfrak{g}=0$ where $\mathfrak{g}$ is solvable. We show that the problem of finding a smooth map $ρ:M\to G$, where $G$ is an $n$-dimensional so…

Sharp conditions found for solving heat equation on Riemannian manifolds.

We analyze symplectic forms on six dimensional real solvable and non-nilpotent Lie algebras. More precisely, we obtain all those algebras endowed with a symplectic form that decompose as the direct sum of two ideals or are indecomposable solvable algebras with a four dimensional nilradical.

Study finds index of symmetry for solvable 3D Lie groups with left-invariant metrics.

Study solves equations on tori for Calabi-Yau problems.

The main contribution of our paper is to give a partial classification of the quasi-exactly solvable Lie algebras of first order differential operators in three variables, and to show how this can be applied to the construction of new quasi-exactly solvable Schrödinger operators in three dimensions.

Classifies two-step solvable Lie groups with SKT structures.

In this paper we try to generalize the Haefliger theorem on completly solvable Lie foliations. We prove that: every completely solvable Lie foliation on a compact manifold is the inverse image of a homogenus foliation. Every manifold in this paper is compact and our Lie group G is connexe and simply connexe.

Optimizes trading strategy for cointegrated assets with bounded risk.

Study of translators in solvable group, finding new examples and non-existence.

Classifies solvable symplectic Lie algebras via extensions and proves structural theorems.

We present an approach to solvable pseudo-Riemannian symmetric spaces based on papers of M.Cahen, M.Parker and N.Wallach. Thereby we reproduce the classification of solvable symmetric triples of Lorentzian signature $(1,n-1)$ and complete the case of signature $(2,n-2)$. Moreover we discuss the topology of non-simply-c…

Paper generalizes results from nilpotent Lie algebras to broader types.

We give a new proof that compact infra-solvmanifolds with isomorphic fundamental groups are smoothly diffeomorphic. More generally, we prove rigidity results for manifolds which are constructed using affine actions of virtually polycyclic groups on solvable Lie groups. Our results are derived from rigidity properties o…

Classifies 2-solvable Frobenius Lie algebras based on endomorphisms.

We establish several new results about both the (n)-solvable filtration, F_n^m, of the set of link concordance classes and the (n)-solvable filtration of the string link concordance group. We first establish a relationship between Milnor's invariants and links, L, with certain restrictions on the 4-manifold bounded by …

Classical solvable stochastic volatility models (SVM) use a CEV process for instantaneous variance where the CEV parameter $γ$ takes just few values: 0 - the Ornstein-Uhlenbeck process, 1/2 - the Heston (or square root) process, 1- GARCH, and 3/2 - the 3/2 model. Some other models were discovered in \cite{Labordere2009…

We show that the Membership Problem for finitely generated subgroups of 3-manifold groups is solvable.