In this paper, the dual Orlicz curvature measure is proposed and its basic properties are provided. A variational formula for the dual Orlicz-quermassintegral is established in order to give a geometric interpretation of the dual Orlicz curvature measure. Based on the established variational formula, a solution to the …
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.
169,051 papers · 148 categories
Trend · papers per month
48 results for “dual Orlicz curvature measure”
The general volume of a star body, a notion that includes the usual volume, the th dual volumes, and many previous types of dual mixed volumes, is introduced. A corresponding new general dual Orlicz curvature measure is defined that specializes to the -dual curvature measures introduced recently by Lutwak, Ya…
New method solves a generalized Minkowski problem using a curvature flow.
problem Generalized Minkowski problem for smooth measures.
method Flow involving Gauss curvature and support function.
result Existence of solutions for the dual Orlicz-Minkowski problem.
Study anisotropic inverse Gauss curvature flows and solve dual Orlicz Minkowski problems.
problem Solving dual Orlicz Minkowski problems for anisotropic flows.
method Anisotropic inverse Gauss curvature flows and stationary solutions.
result New existence results for dual Orlicz Minkowski problems for smooth measures.
Extends dual volume and curvature measures to broader functions and sets, solving Minkowski problems.
problem Characterize measures for which there exists a convex body with a given dual Orlicz curvature measure.
method Extends dual volume and curvature measures to broader functions and sets, proving existence and existence of solutions for Minkowski problems.
result Existence of convex polytopes and solutions for Minkowski problems when measures are discrete or even.
Smooth even solutions found for a generalized convex geometry problem.
problem Dual Orlicz-Minkowski problem in convex geometry.
method Geometric flow involving Gauss curvature and normal vectors.
result Existence of smooth even solutions for smooth even measures.
Study anisotropic flows without global terms and solve dual Orlicz Christoffel-Minkowski problems.
problem Anisotropic flows without global forcing terms and dual Orlicz Christoffel-Minkowski problems.
method Existence results for dual Orlicz Christoffel-Minkowski type problems via stationary solutions of anisotropic flows.
result Existence results for a class of dual Orlicz Christoffel-Minkowski type problems.
This paper develops basic setting for the dual Orlicz-Brunn-Minkowski theory for star bodies. An Orlicz -radial addition of two or more star bodies is proposed and related dual Orlicz-Brunn-Minkowski inequality is established. Based on a linear Orlicz -radial addition of two star bodies, we derive a f…
This paper introduces the dual Orlicz-Brunn-Minkowski theory for star sets. A radial Orlicz addition of two or more star sets is proposed and a corresponding dual Orlicz-Brunn-Minkowski inequality is established. Based on a radial Orlicz linear combination of two star sets, a formula for the dual Orlicz mixed volume is…
This paper aims to develop basic theory for the dual Orlicz affine and geominimal surface areas for star bodies, which belong to the recent dual Orlicz-Brunn-Minkowski theory for star bodies. Basic properties for these new affine invariants will be provided. Moreover, related Orlicz affine isoperimetric inequalit…
The paper analyzes elicitability of return risk measures and their scoring functions.
problem Elicitability of return risk measures and their scoring functions.
method Dual representation results for convex and geometrically convex return risk measures, axiomatic characterizations of Orlicz premia, and construction of strictly consistent scoring functions.
result Orlicz premia are the only elicitable return risk measures under different sets of conditions.
A new method for transporting unbalanced measures on graphs efficiently.
problem Optimal transport for measures with unequal total masses on graph metric spaces.
method Developed a novel variant of entropy partial transport (Orlicz-EPT) with Orlicz geometric structure, leading to Orlicz-Sobolev transport (OST).
result OST can be efficiently computed by solving a univariate optimization problem, significantly faster than Orlicz-EPT.
Paper solves a generalized chord Minkowski problem using Gauss curvature flows.
problem Generalized chord Minkowski problem using Orlicz functions.
method Gauss curvature flows to achieve existence of smooth solutions.
result Existence of smooth solutions to the orlicz chord Minkowski problem.
This paper solves the dual Minkowski problem for q-torsional rigidity.
problem The dual Minkowski problem for q-torsional rigidity.
method Introduced the p-th dual q-torsional measure and solved the p-th dual Minkowski problem for q-torsional rigidity using a Gauss curvature flow.
result Existence of smooth even and non-even solutions to the p-th dual Minkowski problem for q-torsional rigidity.
Investigates stability properties of Haezendonck-Goovaerts premium principles in Orlicz spaces.
problem Stability properties of Haezendonck-Goovaerts premium principles in various Orlicz spaces.
method Analysis of stability properties including Fatou and Lebesgue properties, and continuity with respect to -weak convergence.
result Haezendonck-Goovaerts principles satisfy the Fatou property and Lebesgue property under certain conditions.
We identify a large class of Orlicz spaces for which the topology fails the C-property introduced in [7]. We also establish a variant of the C-property and use it to prove a -representation theorem for proper convex increasing functionals on dual Banach lattices that satisfy a suitable version …
Paper studies convex risk measures linked to optimization.
problem Risk assessment in finance and insurance.
method Investigates a wide class of risk measures on Orlicz spaces.
result Characterizes the dual of risk measures and provides complementary representations.
Generalized Orlicz premiaq-fin.RM
Introduces generalized Orlicz premia for broader applicability.
problem Developing a flexible framework for insurance premium calculation.
method Introduces a generalized Orlicz premium definition using non-convex loss functions.
result Generalized Orlicz premia encompass various specific cases and maintain key properties.
Closedness of convex sets in Orlicz spaces with applications to dual representation of risk measuresq-fin.MF
Let be a conjugate pair of Orlicz functions. A set in the Orlicz space is said to be order closed if it is closed with respect to dominated convergence of sequences of functions. A well known problem arising from the theory of risk measures in financial mathematics asks whether order closedness of a conve…
Paper solves Musielak-Orlicz-Gauss image problem using parabolic flows.
problem Characterize Musielak-Orlicz-Gauss image measure of convex bodies.
method Study of parabolic flows and approximation technique.
result Provides solutions to the extended Musielak-Orlicz-Gauss image problem.
Study timelike Ricci curvature bounds via optimal transport with Orlicz-type costs.
problem Characterize timelike Ricci curvature bounds.
method Optimal transport with Orlicz-type costs, convexity of relative entropy.
result Characterize timelike Ricci curvature lower bounds via convexity of relative entropy.
Paper solves Orlicz-Aleksandrov problem using Gauss curvature flow.
problem Orlicz-Aleksandrov problem
method Gauss curvature flow
result Existence of smooth solutions
Introduces GG-convex risk measures and derives their dual representations.
problem Defining and studying GG-convex risk measures.
method Introduces GG-convex conjugate, derives dual representations, and studies Orlicz risk measures.
result Derives a general dual representation for GG-convex risk measures.
In the dual of a -Orlicz space , that we call a dual Orlicz space, we show that a proper (resp. finite) convex function is lower semicontinuous (resp. continuous) for the Mackey topology if and only if on each order interval (), it is lowe…
Paper solves capillary Orlicz-Minkowski problem with new inequalities.
problem Finding capillary convex bodies with prescribed Orlicz surface area measures.
method Continuity method and inequalities to solve the capillary even Orlicz-Minkowski problem.
result Volume-normalized smooth solutions and inequalities established.
Study of a flow related to the Orlicz-Minkowski problem for convex hypersurfaces.
problem Orlicz-Minkowski problem involving Gauss curvature and support function.
method Generalized Gauss curvature flow for convex hypersurfaces in Euclidean n-space.
result Long-time existence and convergence of the flow, leading to existence results for the Orlicz-Minkowski problem.
Orlicz-Minkowski flowsmath.DG
Study anisotropic flows solving Orlicz-Minkowski problems, proving existence and new results.
problem Anisotropic non-homogeneous Gauss curvature flows and Orlicz-Minkowski problems.
method Long-time existence and behavior analysis, parabolic approximation method, curvature flow.
result Existence and new results for Orlicz-Minkowski problems, including versions.
Study an anisotropic capillary flow to solve capillary Orlicz-Minkowski problem.
problem Solve capillary Orlicz-Minkowski problem without evenness assumption.
method Analyze an anisotropic capillary Gauss curvature flow to prove convergence and establish existence.
result Establish existence result for capillary Orlicz-Minkowski problem without evenness assumption.
Study proves only origin-centered spheres solve certain curvature problems.
problem Proving uniqueness of solutions to curvature problems.
method Using the Heintze-Karcher inequality, the study proves the uniqueness of smooth, strictly convex solutions to a class of Minkowski type problems.
result Only origin-centered spheres solve isotropic and -Gaussian-Minkowski problems.
New method solves generalized Minkowski problem for torsional rigidity.
problem Generalized Minkowski problem for torsional rigidity.
method Flow method
result Existence of solutions for general measures.
Novel Orlicz regrets consistently bound environmental variable statistics.
problem Consistent evaluation of stochastic environmental variables like water quality indices.
method Proposed novel Orlicz regrets for upper and lower bounds.
result Explicit linkage between Orlicz regrets and divergence risk measures.
Paper solves Minkowski problem for q-torsional rigidity using curvature flow.
problem Solving Minkowski problem for q-torsional rigidity.
method Method of curvature flows.
result Existence of smooth non-even solutions.
We provide a variety of results for (quasi)convex, law-invariant functionals defined on a general Orlicz space, which extend well-known results in the setting of bounded random variables. First, we show that Delbaen's representation of convex functionals with the Fatou property, which fails in a general Orlicz space, c…
Improves risk and variability measures continuity and consistency.
problem Improving the continuity and consistency of risk and variability measures.
method Analyzes convex and order bounded above functionals on Frechet lattices and Orlicz spaces.
result Order-continuous, law-invariant functionals on Orlicz spaces are strongly consistent everywhere.
Paper bounds Kähler manifolds' diameter using Orlicz spaces and complex Monge-Ampère equations.
problem Establishing diameter bounds for Kähler manifolds in Orlicz spaces.
method Proving a priori estimates for solutions of complex Monge-Ampère equations in Orlicz spaces using Kołodziej's and Guo-Phong-Tong-Wang's approaches.
result Uniform estimates for Green's function and its gradient for Kähler metrics.
A new statistical model uses Orlicz-Sobolev spaces with Gaussian weight.
problem Statistical modeling of infinite-dimensional probability measures.
method Affine statistical bundle on Gaussian Orlicz-Sobolev space.
result Provides tools for solving infinite-dimensional evolution problems.
Generalizes Sobolev IPM for graph-based measures using Orlicz geometric structure.
problem Limitation of Le et al. (2025) framework to geometry.
method Generalizes Sobolev IPM through Orlicz geometric structure, employing convex functions to capture nuanced geometric relationships.
result GSI-M reduces to a simple univariate optimization problem, achieving remarkable computational efficiency.
Surplus-invariant risk measuresq-fin.MF
This paper presents a systematic study of the notion of surplus invariance, which plays a natural and important role in the theory of risk measures and capital requirements. So far, this notion has been investigated in the setting of some special spaces of random variables. In this paper we develop a theory of surplus …
Neural networks can approximate functions uniformly across various measures.
problem Universal approximation of functions across different probability measures.
method Proving neural networks are dense in Orlicz spaces, extending classical theorems.
result Neural networks uniformly approximate functions for weakly compact families of measures.
Calculations of Orlicz cohomology for simple manifolds and related inequalities.
problem Understanding Orlicz cohomology and inequalities for basic manifolds.
method Calculations of Orlicz cohomology for real line, hyperbolic plane, and ball; discussion of inequalities.
result Relationship between Orlicz cohomology and Poincaré--Sobolev--Orlicz inequalities.
The paper characterizes risk measures with the Fatou property in function spaces.
problem Investigating the Fatou property of law-invariant risk measures in function spaces.
method Characterization of the Fatou property using the AOCEA property and dual representations.
result Risk measures with the Fatou property exist under the AOCEA property in most classical model spaces.
Derives stability for curvature measure near constant density, proving dual Minkowski problem solutions.
problem Stability of curvature measure near constant density
method Derives stability result for curvature measure, proves existence and uniqueness of solutions to dual Minkowski problem.
result Existence and uniqueness of solutions to dual Minkowski problem for positive indices, stability result for curvature measure.
Unified Minkowski problem discussed for (p,q)-mixed quermassintegrals.
problem Unified Minkowski problem for (p,q)-mixed quermassintegrals.
method Introducing (p,q)-mixed quermassintegrals and (p,q)-dual mixed curvature measure to study the Minkowski problem.
result Derivation of important properties and geometric inequalities for (p,q)-mixed quermassintegrals.
The Orlicz-Petty bodiesmath.MG
This paper is dedicated to the Orlicz-Petty bodies. We first propose the homogeneous Orlicz affine and geominimal surface areas, and establish their basic properties such as homogeneity, affine invariance and affine isoperimetric inequalities. We also prove that the homogeneous geominimal surface areas are continuous, …
New risk measure extensions preserve key properties.
problem Extending risk measures to larger spaces while preserving properties.
method Unique extension of dilatation monotone risk measures to .
result Risk measures extend uniquely and preserve monotonicity, convexity, and cash-additivity.
SL(n) covariant valuations on Orlicz spaces are represented and characterized.
problem Representing SL(n) covariant valuations on Orlicz spaces.
method Representation theorem established for continuous, SL(n) covariant vector-valued valuations.
result Unique characterization of SL(n) covariant valuations as moment vectors.
We construct an infinite-dimensional information manifold based on exponential Orlicz spaces without using the notion of exponential convergence. We then show that convex mixtures of probability densities lie on the same connected component of this manifold, and characterize the class of densities for which this mixtur…
The Orlicz-Brunn-Minkowski theory receives considerable attention recently, and many results in the -Brunn-Minkowski theory have been extended to their Orlicz counterparts. The aim of this paper is to develop Orlicz affine and geominimal surface areas for single convex body as well as for multiple convex bod…