arXiv research

In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the marginal distribution of the process itself. This technique is an extension of the classical reflection principle for Brownian motion, and it is o…

After establishing the uniqueness of the continuation of local Cauchy data for harmonic maps between two Riemannian manifolds M and N, we prove (i) a reflection principle for a smooth minimal submanifold Y of a Riemannian manifold M that contains a reflective submanifold of M as a hypersurface and (ii) the reflection p…

Paper investigates reflection principles for zero mean curvature surfaces in isotropic 3-space.

Minimal surfaces reflect across spheres, proving annulus uniqueness.

We give a proof of the classical Schwarz reflection principle for Jenkins-Serrin type minimal surfaces in the homogeneous three manifolds $E(κ, τ)$ for $κ\leqslant 0$ and $τ\geqslant 0$. In our previous paper we proved a reflection principle in Riemannian manifolds. The statements and techniques in the two papers are d…

The paper studies large deviation principles for stochastic volatility models with reflection, focusing on binary barrier options and call prices.

On a multi-assets Black-Scholes economy, we introduce a class of barrier options. In this model we apply a generalized reflection principle in a context of the finite reflection group acting on a Euclidean space to give a valuation formula and the semi-static hedge.

We prove a reflection principle for minimal surfaces in smooth (non necessarily analytic) three manifolds and we give an explicit application when the ambient space is just a smooth manifold.

The paper calculates prices for multi-step barrier options under the Black-Scholes model.

As in the case of minimal surfaces in the Euclidean 3-space, the reflection principle for maximal surfaces in the Lorentz-Minkowski 3-space asserts that if a maximal surface has a spacelike line segment $L$, the surface is invariant under the $180^\circ$-rotation with respect to $L$. However, such a reflection property…

The paper creates symmetrical discrete minimal nets using Schwarz reflection.

We solve the partial data Calderón problem for the connection Laplacian on Riemann surfaces.

This paper continues arXiv.org:math.AG/0609256, arXiv:0708.3991 and arXiv:0710.0162 . Using authors's methods of 1980, 1981, some explicit finite sets of number fields containing all ground fields of arithmetic hyperbolic reflection groups in dimension at least 3 are defined, and explicit bounds of their degrees (over …

An analytico-geometric reflection principle is established by means of normal deformations of analytic discs.

New distance comparison principle for curve shortening flow in higher dimensions.

We build an elementary analytico-geometric theory of Segre chains and their jets.

In the present paper, we associate the techniques of the Lewy-Pinchuk reflection principle with the Behnke-Sommer continuity principle. Extending a so-called reflection function to a parameterized congruence of Segre varieties, we are led to studying the envelope of holomorphy of a certain domain covered by a smooth Le…

Generalizes Fermat's principle for wave propagation in cone structures.

This work accelerates constrained sampling using large deviation principles.

Bayesian RL enhances LLMs to reflectively explore and correct errors.

We introduce the concept of singular recursive utility. This leads to a kind of singular BSDE which, to the best of our knowledge, has not been studied before. We show conditions for existence and uniqueness of a solution for this kind of singular BSDE. Furthermore, we analyze the problem of maximizing the singular rec…

Reflected Diffusion Models improve on score-based models by incorporating data constraints.

Develops non-Markovian couplings for sub-Riemannian Brownian motions.

We give a necessary and sufficient condition for the smooth extension of a diffeomorphism between smooth strictly pseudoconvex domains in four real dimensional almost complex manifolds. The proof is mainly based on a reflection principle for pseudoholomorphic discs, on precise estimates of the Kobayashi-Royden infinite…

Large deviation principles for multivariate stochastic volatility models.

We propose a new model for digital pathology segmentation, based on the observation that histopathology images are inherently symmetric under rotation and reflection. Utilizing recent findings on rotation equivariant CNNs, the proposed model leverages these symmetries in a principled manner. We present a visual analysi…

This is an extensive (published) survey on CR geometry, whose major themes are: formal analytic reflection principle; generic properties of Systems of (CR) vector fields; pairs of foliations and conjugate reflection identities; Sussmann's orbit theorem; local and global aspects of holomorphic extension of CR functions;…

Study curve shortening flow in high dimensions with boundary constraints.

The goal of this work is to establish a proof of the Gromov convergence in Hoelder spaces for curves with a totally real boundary condition following the original geometric idea of Gromov. We use a local reflection principle in neighbourhoods of the totally real submanifold as developed by Ivashkovich and Shevchishin a…

This paper is devoted to a systematic study of the geometry of nondegenerate $\bbR^n$-actions on $n$-manifolds. The motivations for this study come from both dynamics, where these actions form a special class of integrable dynamical systems and the understanding of their nature is important for the study of other Hamil…

Foundations for free boundary Brakke flows established.

We use the weighted Hsiung-Minkowski integral formulas and Brendle's inequality to show new rigidity results. First, we prove Alexandrov type results for closed embedded hypersurfaces with radially symmetric higher order mean curvature in a large class of Riemannian warped product manifolds, including the Schwarzschild…

Study on curve shortening flow with boundary conditions, proving convergence or contraction.

In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call symmetry property and the duality principle in option pricing. A particular atten…

We consider embedded ring-type surfaces (that is, compact, connected, orientable surfaces with two boundary components and Euler-Poincaré characteristic zero) in ${\bold R}^3$ of constant mean curvature which meet planes $Π_1$ and $Π_2$ in constant contact angles $γ_1$ and $γ_2$ and bound, together with those planes, a…

A new insurance and reinsurance pricing scheme based on realized loss.

New approach tackles nonidentifiability in nonlinear blind source separation.

In this paper we develop a global correspondence between immersed horospherically convex hypersurfaces in hyperbolic space and complete conformal metrics on domains in the sphere. We establish results on when the hyperbolic Gauss map is injective and when an immersed horospherically convex hypersurface can be unfolded …

Framework for confidence estimation in deep CT reconstructions.

CurveRL optimizes large model reasoning by reweighting prompts based on their rank and density.

FinReflectKG - EvalBench benchmarks financial KG extraction from SEC 10-K filings.

A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical methods that enable the coherent propagation of probabilities through a (possibly dete…

A discrete subgroup of the group of isometries of the hyperbolic space is called reflective if up to a finite index it is generated by reflections in hyperplanes. The main result of this paper is a complete classification of the reflective (and quasi-reflective) subgroups among the Bianchi groups and their extensions.

New method produces reflections with nonseparating fixed points.

Survey explores interactions between four conformal dynamics branches.

One reflection suffices for orthogonal weights, reducing GPU usage.

Minimal surfaces in 3-sphere created by reflections from polygons, with new examples based on pentagons.

Study thin hyperbolic reflection groups and their properties.