arXiv research

Investigates optimal execution under time-varying liquidity, preventing price manipulation.

This book provides a detailed introduction to linear wave equations on Lorentzian manifolds (for vector-bundle valued fields). After a collection of preliminary material in the first chapter one finds in the second chapter the construction of local fundamental solutions together with their Hadamard expansion. The third…

Paper solves local well-posedness for Schrödinger flow into sphere with natural boundary conditions.

The paper proves well-posedness of nonlocal PDEs related to stochastic control problems.

(Working Paper) Using a purely probabilistic argument, we prove the global well-posedness of multidimensional superquadratic backward stochastic differential equations (BSDEs) without Markovian assumption. The key technique is the interplay between the local well-posedness of fully coupled path-dependent forward backwa…

The paper derives expansions for Green's operators and resolvents using Hadamard methods.

Harmonic maps between pinched Hadamard surfaces are quasi-conformal.

New insights into identifying mixtures of product distributions using Hadamard extensions.

Study proves well-posedness and scattering for wave equations on hyperbolic spaces with singular data.

Cyclic projections in Hadamard spaces can be irregular, unlike in Hilbert spaces.

Study shows spectrum properties for specific Hadamard manifolds.

Sharp curvature inequality extends Euclidean isoperimetric inequality to Cartan-Hadamard manifolds.

Study well-posedness of SPDE on Riemannian manifolds with rough initial conditions.

A new class of harmonic Hadamard manifolds, those spaces called of hypergeometric type, is defined in terms of Gauss hypergeometric equations. Spherical Fourier transform defined on a harmonic Hadamard manifold of hypergeometric type admits an inversion formula. A characterization of harmonic Hadamard manifold being of…

The paper provides formulas for Hadamard coefficients using Green's operators.

We study the question of well-posedness of the Cauchy problem for Schrödinger maps from $\rone \times \rtwo$ to the sphere $\stwo$ or to ${\mathbb H^2}$, the hyperbolic space. The idea is to choose an appropriate gauge change so that the derivatives of the map will satisfy a certain nonlinear Schrödinger system of equa…

Gradient flow on diffeomorphisms for image registration, with well-posedness proven.

Formula for Hadamard coefficients from Green's operators on spacetimes.

Upper bounds for circumradius in Hadamard surfaces with curvature constraints.

The subject of this article is the introduction of a new concept of well-posedness of Bayesian inverse problems. The conventional concept of (Lipschitz, Hellinger) well-posedness in [Stuart 2010, Acta Numerica 19, pp. 451-559] is difficult to verify in practice and may be inappropriate in some contexts. Our concept sim…

We establish both local and global well-posedness for the heat flow of polyharmonic maps from $R^n$ to a compact Riemannian manifold without boundary for initial data with small BMO norms.

Solves Plateau problem for surfaces in pinched curvature manifolds.

Proves Hadamard states for Dirac fields on manifolds with timelike boundaries.

In this paper, we study the well-posedness of boundary value problems for a special class of degenerate elliptic equations coming from geometry. Such problems is intimately tied to rigidity problem arising in infinitesimal isometric deformation, The characteristic form of this class of equations is changing its signs i…

Various results based on some convexity assumptions (involving the exponential map along with affine maps, geodesics and convex hulls) have been recently established on Hadamard manifolds. In this paper we prove that these conditions are mutually equivalent and they hold if and only if the Hadamard manifold is isometri…

Proves well-posedness of gradient solitons on bundle gerbe.

The commuting vector fields approach, devised for strichartz estimates in [13], was developed for proving the local well-posedness in the Sobolev spaces $H^s$ with $s>2+\frac{2-\sqrt{3}}{2}$ for general quasi-linear wave equation in ${\mathbb R}^{1+3}$ by Klainerman and Rodnianski. Via this approach they obtained the l…

Paper computes link determinants using Fourier-Hadamard transforms.

This paper establish the local (or global, resp.) well-posedness of the heat flow of biharmonic maps from $R^n$ to a compact Riemannian manifold without boundary with small local BMO (or BMO, resp.) norms.

New theorem extends Hadamard's to transversely affine geometry.

Quantizes Maxwell's theory on Lorentzian manifolds via a novel gauge-fixing method.

The paper proves Liouville-type theorems on Hadamard manifolds.

We consider an integro-differential equation derived from a system of coupled parabolic PDE and an ODE which describes an European option pricing with liquidity shocks. We study the well-posedness and prove comparison principle for the corresponding initial value problem.

Maps between Hadamard manifolds are quasi-isometric to harmonic maps.

Proves well-posedness for hard phase model in general relativity.

We establish the global well-posedness of the initial value problem for the Schrodinger map flow for maps from the real line into Kahler manifolds and for maps from the circle into Riemann surfaces. This partially resolves a conjecture of W.-Y. Ding.

In this article we study the class of right-invariant, fractional order Sobolev-type metrics on groups of diffeomorphisms of a compact manifold M. Our main result concerns well-posedness properties for the corresponding Euler-Arnold equations, also called the EPDiff equations, which are of importance in mathematical ph…

The study extends isoperimetric inequalities to non-positive curvature spaces.

Nonexistence of radial optimal functions on certain Cartan-Hadamard manifolds.

Efficient algorithm for Hadamard decomposition of matrices.

Study KKT conditions for multi-objective optimization on Hadamard manifolds.

We use the combinatorial harmonic map theory to study the isometric actions of discrete groups on Hadamard spaces. Given a finitely generated group acting by automorphisms, properly discontinuously and cofinitely on a simplicial complex and its isometric action on a Hadamard space, we formulate criterions for the actio…

Proves homological inequality for cycles in Hadamard spaces of asymptotic rank 2.

Linear inequality found for certain curved spaces.

Paper proves existence of Hadamard states for Maxwell equations.

The paper defines Fenchel conjugate and biconjugate on Hadamard manifolds.

Introduces conformal Bach flow and proves its well-posedness and backward uniqueness.

The article proves isometry theorems for specific types of manifolds.