We present an axiomatic/synthetic account of the Huygens Principle of wave fronts. The primitive notions are "touching", and (a weak notion of ) metric. The paper simplifies some of the exposition of the author's "Metric spaces and SDG", Theory and Appl. of Categories 32 (2017), 803-822
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,742 papers · 148 categories
Trend · papers per month
48 results for “asymptotic Huygens principle”
Solves wave equation on non-flat harmonic manifolds using Abel transform and Fourier analysis.
problem Wave equation on non-flat harmonic manifolds with specific curvature conditions.
method Explicit representation using inverse dual Abel transform and Fourier transform.
result Shows asymptotic Huygens principle and equidistribution of energy.
We prove a Paley-Wiener Theorem for a class of symmetric spaces of the compact type, in which all root multiplicities are even. This theorem characterizes functions of small support in terms of holomorphic extendability and exponential type of their (discrete) Fourier transforms. We also provide three independent new p…
Due to spectral obstructions, a scattering theory in the Lax-Phillips sense for the wave equation for differential p-forms on H^{n+1} cannot be developed. As a consequence, Huygens' principle for the wave equation in this context does not hold. If we restrict the class of forms and we consider the case of coclosed p-fo…
A new model uses Lorentz-Finsler geometry to predict wave propagation.
problem Modeling wave propagation in anisotropic and rheonomic media.
method Identifying wave trajectories as lightlike pregeodesics of a specific Lorentz-Finsler metric, solving ODE systems.
result Wave trajectories can be easily computed in real time.
We extend to the -dimensional case a recent theorem establishing the validity of the Huygens' envelope principle for wavefronts in Finsler spaces. Our results have direct applications in analogue gravity models, for which the Fermat's principle of least time naturally gives origin to an underlying Finslerian geometr…
Wave propagation framework using cone structures and observers' vector fields.
problem Describing classic wave propagation in anisotropic media.
method Introduces a cone structure and an observers' vector field to describe wave propagation.
result Reduces the PDE for wavefronts to ODE for cone geodesics of .
Improved model predicts wildfire spread on slopes.
problem Accurate prediction of wildfire spread on slopes.
method Combines Rothermel model, Huygens' principle, and advanced techniques.
result More precise model of wildfire propagation.
Any surface can be foliated into equipotential hypersurfaces of the level sets. A current result is that the contours are the progressing wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, as well as with a corresponding eikonal equation. The lev…
Stability of catenoid in 4D Minkowski space proven without symmetry assumptions.
problem Stability of the catenoid as a nonflat stationary solution to the HVMC equation in 4D.
method Established asymptotic stability under codimension-1 assumption, using new commutator vector field estimates.
result Catenoid stability in 4D proven without symmetry assumptions, with improved pointwise decay.
Study compares nodal sets of solutions to the Allen-Cahn equation.
problem Comparing nodal sets of solutions to the Allen-Cahn equation with conical asymptotics.
method Maximum principle for linearized operator on unbounded domains.
result Positive phase uniquely determines the solution and enforces global ordering.
Study asymptotic behavior of Weingarten surfaces at infinity.
problem Understanding the behavior of Weingarten surfaces at infinity.
method Derive asymptotic expansion and solve Dirichlet problem.
result Established maximum principle and solved Dirichlet problem.
Study on implied volatility of an affine jump-diffusion model.
problem Characterize implied volatility of an affine jump-diffusion model.
method Explicit moment generating function derived from solving ODEs; large deviation principle applied.
result Asymptotic behaviors of implied volatility in large-maturity and large-strike regimes characterized.
New mass inequalities and proofs for causal variational principles.
problem Proving new mass inequalities for causal variational principles.
method Proved a new inequality for minimizers of causal variational principles and applied it to prove the positive mass theorem.
result Introduced a positive quasilocal mass and proved new mass inequalities.
We use a Lagrangian perspective to show the limiting absorption principle on Riemannian scattering, i.e. asymptotically conic, spaces, and their generalizations. More precisely we show that, for non-zero spectral parameter, the `on spectrum', as well as the `off-spectrum', spectral family is Fredholm in function spaces…
New distance comparison principle for curve shortening flow in higher dimensions.
problem Understanding curve shortening flow in higher dimensions.
method Established a variant of Huisken's distance comparison principle.
result Symmetric curve shortening flow with one-to-one convex projection develops Type I singularities and becomes asymptotically circular.
Improved control approach for correlated bandits with better performance.
problem General multi-armed bandit problem with correlated elements.
method Introducing entropy regularisation to obtain a smooth asymptotic approximation of the value function, leading to a semi-index approximation of the optimal decision process.
result Performance of Asymptotic Randomised Control (ARC) algorithm compares favorably with other approaches.
The paper studies global Yamabe flow on AF manifolds, preserving ADM mass.
problem Existence and behavior of Yamabe flow on AF manifolds.
method New local existence theorem and maximum principle for parabolic equations.
result Global existence of Yamabe flow on AF manifolds with non-negative scalar curvature.
Study on mean curvature flow of graphs in higher dimensions.
problem Analyzing the evolution of graphs under mean curvature flow.
method Derives estimates using a new maximum principle for submanifolds, applies to uniformly area decreasing maps.
result Graphicality and area decreasing property are preserved for uniformly area decreasing maps.
Large deviation principles for multivariate stochastic volatility models.
problem Understanding the behavior of log-processes in multivariate stochastic volatility models.
method Establishing a comprehensive sample path large deviation principle for log-processes.
result Asymptotic formulas for first exit times and barrier option prices derived from the LDP.
The existence and nonexistence of -harmonic functions in unbounded domains of are investigated. We prove that if the Hausdorff measure of the asymptotic boundary of a domain is zero, then there is no bounded -harmonic function of for , where $λ_1(\mathb…
New approach analyzes ancient solutions and singularities of mean curvature flow.
problem Analyzing ancient solutions and singularities of mean curvature flow locally modeled on a cylinder.
method Introduces PDE-ODI principle to convert parabolic differential equations into systems of ordinary differential inequalities.
result Establishes the uniqueness of the bowl soliton times a Euclidean factor among ancient, cylindrical flows with dominant linear mode.
A maximum principle for C^0 null hypersurfaces is obtained and used to derive a splitting theorem for spacetimes which contain null lines. As a consequence of this null splitting theorem, it is proved that an asymptotically simple vacuum (Ricci flat) spacetime which contains a null line is isometric to Minkowski space.
The Ekeland variational principle implies what can be regarded as a strong version, in the category, of the Yau minimum principle: under the appropriate hypotheses {\it every} minimizing sequence admits a {\it good shadow}, a second minimizing sequence that has good properties and is asymptotic to the original on…
In this work we extend the ODE Maximum principle of Hamilton to non-compact hypersurfaces using the Omari-Yau maximum principle at infinity. As an application of this result, we investigate Inverse Mean Curvature Flow (IMCF) of non-compact hypersurfaces in hyperbolic space. Specifically, we look at bounded graphs over …
Unique steady and expanding solitons with spherical links identified.
problem Characterizing steady and expanding Ricci solitons with specific asymptotic symmetries.
method Symmetry principle applied to asymptotically cylindrical and conical GRSs, proving uniqueness for Bryant solitons.
result Bryant steady and expanding solitons are the unique asymptotically cylindrical and conical GRSs with spherical links under certain conditions.
Study of complex Hessian equations using subharmonic functions and geodesics.
problem Understanding geodesics within complex Hessian equations.
method Perron envelope construction, comparison principle, rooftop equality, Kiselman minimum principle.
result Established criterion for geodesic connectivity among -subharmonic functions.
Study harmonic surfaces in 3D space, proving superposition principle.
problem Understanding harmonic surfaces in .
method Using harmonic Enneper immersions and superposition principle.
result Minimal and maximal surfaces can be decomposed into harmonic components.
We discuss the essential self-adjointness of wave operators, as well as the limiting absorption principle, in generalizations of asymptotically Minkowski settings. This is obtained via using a Fredholm framework for inverting the spectral family first, and then refining its conclusions to show its dense range in L^2 wh…
We prove a large deviations principle for the class of multidimensional affine stochastic volatility models considered in (Gourieroux, C. and Sufana, R., J. Bus. Econ. Stat., 28(3), 2010), where the volatility matrix is modelled by a Wishart process. This class extends the very popular Heston model to the multivariate …
New algorithm optimizes contextual bandits with adaptive exploration.
problem Asymptotically suboptimal contextual bandit algorithms.
method Asymptotically optimal algorithm exploiting linear structure, adaptive to context distribution.
result Sub-logarithmic regret in well-behaved context distributions.
A pricing principle is introduced for non-attainable claims in incomplete markets.
problem Pricing non-attainable contingent claims in incomplete markets.
method Distorted Radon-Nikodym derivative and Tsallis relative entropy over a family of equivalent martingale measures.
result The pricing principle is closely related to backward stochastic differential equations and is arbitrage-free and time-consistent.
We will generalize a Maximum Principle at Infinity in the parabolic case given by De Lima [Ann. Global Anal. Geom. , 325-343 2001] and De Lima and Meeks [Indiana Univ. Math. Journal 5, 1211-1223 2004], for disjoints hypersurfaces of with bounded mean curvature without restriction…
Using a maximum principle for self-shrinkers of the mean curvature flow, we give new proofs of a rigidity theorem for rotationally symmetric compact self-shrinkers and a result about the asymptotic behavior of self-shrinkers. This comparison argument also implies a linear bound for the second fundamental form of self-s…
New bandit algorithm maximizes information gain.
problem Optimizing decision-making in uncertain environments.
method Approximates information maximization using entropy and free energy principles.
result Asymptotic optimality proven for two-armed bandit problem.
The aim of this work is to study how the asymptotic boundary of a minimal hypersurface in H^nxR determines the behavior of the hypersurface at finite points, in several geometric situations.
The main result of the paper is a version of the fundamental theorem of asset pricing (FTAP) for large financial markets based on an asymptotic concept of no market free lunch for monotone concave preferences. The proof uses methods from the theory of Orlicz spaces. Moreover, various notions of no asymptotic arbitrage …
We present a number of related comparison results, which allow to compare moment explosion times, moment generating functions and critical moments between rough and non-rough Heston models of stochastic volatility. All results are based on a comparison principle for certain non-linear Volterra integral equations. Our u…
Upper bounds on nullhomotopy volumes in nilpotent spaces are refined.
problem Bounding volumes of nullhomotopies in nilpotent spaces.
method Extension of the Shadowing Principle to nilpotent spaces.
result Improved bounds on nullhomotopy volumes, nearly meeting simply connected settings.
Paper finds properties of special geometric shapes in higher dimensions.
problem Understanding translating solitons for curvature flows.
method Analyzes properties of -translators using maximum principles.
result Uniqueness of strictly convex -translators with a single end.
We prove the equality case of the Penrose inequality in all dimensions for asymptotically flat hypersurfaces. It was recently proven by G. Lam that the Penrose inequality holds for asymptotically flat graphical hypersurfaces in Euclidean space with non-negative scalar curvature and with a minimal boundary. Our main the…
Paper studies apparent horizon dynamics and introduces a null comparison principle.
problem Global dynamics of apparent horizon and local achronality.
method Constructing apparent horizon by solving MOTS along null hypersurfaces, using Klainerman-Szeftel estimates and null comparison principle.
result Smooth, asymptotically null, and converging apparent horizon proven.
Improved estimator reduces bias in statistical learning models.
problem Asymptotic bias in classic WDRO estimator.
method Adjusted Wasserstein distributionally robust estimator.
result Asymptotic unbiased estimator with smaller MSE.
Paper proves uniqueness of catenary cylinders based on their asymptotic shape.
problem Proving uniqueness of catenary cylinders by their asymptotic behavior.
method Applying the moving plane method of Alexandrov and strong maximum principle for elliptic operators.
result Established a uniqueness result for -catenary cylinders based on their asymptotic behavior.
We study fractional stochastic volatility models in which the volatility process is a positive continuous function of a continuous Gaussian process . Forde and Zhang established a large deviation principle for the log-price process in such a model under the assumptions that the function is globally…
New algorithms improve estimation of treatment effects.
problem Estimating Average Treatment Effect (ATE) in adaptive settings.
method Optimistic algorithms for adaptive estimation using AIPW estimator.
result Significant theoretical and empirical gains over prior methods.
We study the small time asymptotics of the gradient and Hessian of the logarithm of the heat kernel at the cut locus, giving, in principle, complete expansions for both quantities. We relate the leading terms of the expansions to the structure of the cut locus, especially to conjugacy, and we provide a probabilistic in…
Datasets are growing not just in size but in complexity, creating a demand for rich models and quantification of uncertainty. Bayesian methods are an excellent fit for this demand, but scaling Bayesian inference is a challenge. In response to this challenge, there has been considerable recent work based on varying assu…