arXiv research

Study abelianization of Lie algebroids and groupoids, providing conditions for existence.

The paper examines conditions for Einstein multiply warped products and estimates their parameters.

Study on existence and structure of P-area surfaces in Heisenberg group.

We formulate a sufficient condition for the existence of a consistent price system (CPS), which is weaker than the conditional full support condition (CFS) introduced by Guasoni, Rasonyi, and Schachermayer [Ann. Appl. Probab., 18(2008), pp. 491-520] . We use the new condition to show the existence of CPSs for certain p…

DG algorithms often fail to generalize well in limited domains, highlighting necessary vs. sufficient conditions.

We derive deterministic criteria for the existence and non-existence of equivalent (local) martingale measures for financial markets driven by multi-dimensional time-inhomogeneous diffusions. Our conditions can be used to construct financial markets in which the \emph{no unbounded profit with bounded risk} condition ho…

Paper investigates curvature problems and existence of solutions.

New existence results for curvature problem on balls with specific conditions.

Study proves optimal controls for stochastic Volterra equations with singular kernels.

Paper proves short-term existence of fractional mean curvature flow.

We provide conditions for the existence and the unicity of strictly stationary solutions of the usual Dynamic Conditional Correlation GARCH models (DCC-GARCH). The proof is based on Tweedie's (1988) criteria, after having rewritten DCC-GARCH models as nonlinear Markov chains. Moreover, we study the existence of their f…

Paper finds conditions for special geometric structures on certain spaces.

Paper finds solutions to a complex equation on surfaces with boundary conditions.

The paper is concerned with the problem of existence of solutions for the Heath-Jarrow-Morton equation with linear volatility. Necessary conditions and sufficient conditions for the existence of weak solutions and strong solutions are provided. It is shown that the key role is played by the logarithmic growth condition…

We study the steady state solutions of a generalized logistic type equation on a complete Riemannian manifold. We provide sufficient conditions for existence, respectively non-existence of positive solutions, which depend on the relative size of the coefficients and their mutual interaction with the geometry of the man…

We prove the existence of metrics maximizing the first eigenvalue normalized by area on closed, non-orientable surfaces assuming two spectral gap conditions. These spectral gap conditions are proved by the authors in \cite{MS3}.

We find a condition for stable asset pricing models.

The paper studies Ricci flow on manifolds with boundary, proving existence, uniqueness, and boundary conditions preservation.

The paper finds sign-changing solutions for a specific type of elliptic equation.

We consider the existence problem for `Steiner networks' (trivalent graphs with 120 degree angles at each junction) in strictly convex domains, with `Neumann' boundary conditions (orthogonal intersection with the domain boundary.) For each of the three possible combinatorial possibilities, sufficient conditions on the …

Proves existence of proper solutions for inverse mean curvature flow.

New method improves meta-learning performance by task-specific initialization.

Novel boundary conditions for Ricci flow to deform compact manifolds.

Paper classifies non-loose knots and discusses conditions for their existence.

Proves existence of Kähler-Einstein metrics with certain twisting forms.

CSDI improves time series imputation by 40-65% over existing methods.

Study short-time existence of Ricci-DeTurck flow from rough metrics with Morrey-type integrability.

Investigates conditional Chisini means and their application to risk measures.

We introduce several sufficient conditions to guarantee the existence of the Milnor vector field for new classes of singularities of map germs. This special vector field is related with the equivalence problem of the Milnor fibrations for real and complex singularities, if they exit.

When dealing with Heston's stochastic volatility model, the change of measure from the subjective measure P to the objective measure Q is usually investigated under the assumption that the Feller condition is satisfied. This paper closes this gap in the literature by deriving sufficient conditions for the existence of …

In the problem of optimal investment with utility function defined on $(0,\infty)$, we formulate sufficient conditions for the dual optimizer to be a uniformly integrable martingale. Our key requirement consists of the existence of a martingale measure whose density process satisfies the probabilistic Muckenhoupt $(A_p…

Study proves mean curvature flow in GRW spacetimes with perpendicular boundary condition.

We consider an economy where agents' consumption sets are given by the cone $\mathbf{L}^0_+$ of non-negative measurable functions and whose preferences are defined by additive utilities satisfying the Inada conditions. We extend to this setting the results in \citet{Dana:93} on the existence and uniqueness of Arrow-Deb…

The paper proves existence of horo-convex hypersurfaces in hyperbolic space with specific curvature conditions.

Let $ψ$ be a given function defined on a Riemannian space. Under what conditions does there exist a compact starshaped hypersurface $M$ for which $ψ$, when evaluated on $M$, coincides with the $m-$th elementary symmetric function of principal curvatures of $M$ for a given $m$? The corresponding existence and uniqueness…

We introduce a more restrictive version of the strict $CD(K,\infty)$ -condition, the so-called very strict $CD(K,\infty)$ -condition, and show the existence of optimal maps in very strict $CD(K,\infty)$ -spaces despite the possible lack of uniqueness of optimal plans.

The study finds conditions for Kaehler-Einstein and cscK metrics on certain manifold coverings.

Existence of solutions to the Heath-Jarrow-Morton equation of the bond market with linear volatility and general Lévy random factor is studied. Conditions for existence and non-existence of solutions in the class of bounded fields are presented. For the existence of solutions the Lévy process should necessarily be with…

We investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in $M\times \mathbb R_+$, where $M$ is a complete noncompact Riemannian manifold. Under specific assumptions, we establish existence of solutions satisfying prescribed conditions at infinity, depending on the…

Study on complex line fields on almost-complex manifolds, proving existence conditions.

Paper proves existence of unique constant scalar curvature Kähler metric under certain conditions.

Cosmological singularity theorems such as that of Hawking and Penrose assume local curvature conditions as well as global ones like the existence of a compact (achronal) slice. Here, we prove a new singularity theorem for chronological spacetimes that satisfy what we call a `past null focusing' condition. Such a condit…

A rational projective plane ($\mathbb{QP}^2$) is a simply connected, smooth, closed manifold $M$ such that $H^*(M;\mathbb{Q}) \cong \mathbb{Q}[α]/\langle α^3 \rangle$. An open problem is to classify the dimensions at which such a manifold exists. The Barge-Sullivan rational surgery realization theorem provides necessar…

The study finds nondegenerate harmonic 1-forms using symmetry conditions.

We show that a connection with skew-symmetric torsion satisfying the Einstein metricity condition exists on an almost contact metric manifold exactly when it is D-homothetic to a cosymplectic manifold. In dimension five, we get that the existence of a connection with skew torsion satisfying the Einstein metricity condi…

We construct maximal hypersurfaces with a Neumann boundary condition in Minkowski space via mean curvature flow. In doing this we give general conditions for long time existence of the flow with boundary conditions with assumptions on the curvature of a the Lorentz boundary manifold.

Noncommutatively deformed geometries, such as the noncommutative torus, do not exist generically. I showed in a previous paper that the existence of such a deformation implies compatibility conditions between the classical metric and the Poisson bivector (which characterizes the noncommutativity). Here I present anothe…

The study identifies conditions for algorithms to have tight generalization bounds.