New geometric measure simplifies complex analysis.
problem Complex geometric analysis challenges.
method Geometric integration and convergence methods.
result Smallest measure satisfying Area Formula.
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.
169,341 papers · 148 categories
Trend · papers per month
48 results for “Geometric Measures”
Study on geometric Jensen-Shannon divergence for Gaussian measures in Hilbert space.
problem Computing divergence between Gaussian measures in infinite-dimensional Hilbert space.
method Closed form expression and regularization for divergence calculation.
result Closed form expression and regularization for Geometric Jensen-Shannon divergence.
Generalizes entropy-drift inequality for specific geometric spaces.
problem Entropy, drift, and critical exponent in Gibbs measures on geometrically finite manifolds.
method Generalization of Guivarc'h's inequality for CAT(-1) spaces, analysis of random walks.
result Equality in entropy-drift inequality achieved if and only if Gibbs density is equivalent to hitting measure.
New statistical measures assess group separability in low-dimensional geometrical spaces.
problem Lack of statistical measures to evaluate group separability in low-dimensional geometrical spaces.
method Proposed three statistical measures (PSI-ROC, PSI-PR, PSI-P) based on Projection Separability rationale.
result Statistical-based measures outperform traditional cluster validity indices in evaluating group separability.
Geometrically proves majorizing measure theorem on Hadamard manifolds.
problem Volume size relation between random process index space and its convex hull.
method Assumed Hadamard manifold, derived upper bound for volume ratio, applied to prove majorizing measure theorem.
result Upper bound for volume ratio between index space and convex hull.
Geometrically convex return risk measures on AM-algebras
problem Quantifying risk in time series analysis
method Extending return risk measures to general ordered vector spaces
result Establishing results on finiteness, continuity, separability, and dual and aggregation-based representations
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.
We simplify complex geometric structures for contracting measurable systems.
problem Normal forms for contracting measurable cocycles and foliations.
method Differential-geometric approach to obtain resonance polynomial normal forms via changes of coordinates.
result Obtained nonstationary invariant differential-geometric structures for contracting systems and foliations.
Geometric mean and geodesics defined on probability measures space.
problem Defining and analyzing geometric mean and geodesics in probability measures space.
method Using Fisher information metric, defined geometric mean, and geodesics.
result Geodesics are minimal and uniquely join any two points in probability measures space.
Kernel-based algorithms improve integral estimation with near-geometric speed.
problem Estimating integrals with target measures that are nearly atomic.
method Weighted kernel herding and sequential Bayesian quadrature.
result Near-geometric rate of convergence for nearly atomic target measures.
Geometric BSDEsmath.PR
Develops geometric BSDEs for modeling dynamic return risk measures.
problem Modeling continuous-time dynamic return risk measures.
method Introduces and develops Geometric Backward Stochastic Differential Equations (GBSDEs) and two-driver BSDEs.
result Establishes existence, regularity, uniqueness, and stability of solutions to GBSDEs.
This paper introduces Hausdorff measure and its applications in fractal geometry.
problem Defining and applying Hausdorff measure to fractal geometry.
method Definition of Hausdorff outer measure, Caratheodory's criterion, construction of Hausdorff measure, and introduction of Hausdorff dimension.
result Demonstrates the Hausdorff dimension of the Cantor ternary set.
Study on random surfaces in hyperbolic 3-manifolds, focusing on geometric and topological properties.
problem Distribution of nearly geodesic surfaces in hyperbolic 3-manifolds.
method Invariant measures on the Grassmann bundle G(M) derived from limits of random minimal surfaces.
result Topological limiting measures are totally scarring if M contains a totally geodesic subsurface, while geometrical limiting measures are not.
The Monge-Cayley-Salmon theorem is extended for ruled submanifolds.
problem Generalization of a classical theorem for ruled submanifolds.
method Elementary geometric measure theory.
result Generalization of the Monge-Cayley-Salmon theorem proved.
Proofs a theorem using basic geometric tools.
problem C2-rectifiability problem
method Elementary geometric measure theory and topology
result Gives a proof of Alberti's Luzin-type theorem
Defines a geometric dimension for Lorentzian spaces, distinguishing spacelike and null subspaces.
problem No specific problem stated; focuses on defining a new geometric dimension.
method Introduces a one-parameter family of volume measures and a doubling condition for causal diamonds.
result Defines a geometric dimension for synthetic spacetimes, distinguishing between spacelike and null subspaces.
Study various complexity measures of curves on surfaces.
problem Measuring complexity of curves on surfaces.
method Examines minimum intersections, lengths of words, and covering degrees.
result Established relationships between these complexity measures.
Geometric approach to majorizing measures for polyhedra and general compact objects.
problem Understanding the relationship between a space and its convex hull in geometric measure theory.
method Geometric approach using covering number relationships and volume ratios.
result Established a method to evaluate covering number and volume ratios for various spaces.
Geometric expectiles generalize expectiles for multivariate data.
problem Generalizing expectiles for multivariate distributions.
method Convex risk minimization problem solution for d-dimensional vectors.
result Geometric expectiles are consistent risk measures under common transformations.
Fractal Lipschitz-Killing curvature measures C^f_k(F,.), k = 0, ..., d, are determined for a large class of self-similar sets F in R^d. They arise as weak limits of the appropriately rescaled classical Lipschitz-Killing curvature measures C_k(F_r,.) from geometric measure theory of parallel sets F_r for small distances…
New measure of maximal entropy found for a class of geometrically finite groups.
problem Finding a measure of maximal entropy for relatively Anosov groups.
method Constructing reparameterizations and using exponential expansion along unstable foliations.
result The Bowen-Margulis-Sullivan measure is finite and unique for relatively Anosov groups.
This paper proposes a new geometric framework for asset pricing.
problem The asymmetry between risk-neutral and physical measures in asset pricing.
method Information geometry, focusing on the relativity of probabilistic reference frames.
result Unified explanation for price fluctuations, event-driven behavior, and risk premia.
The volume of a credal set correlates with epistemic uncertainty in binary classification but not in multi-class.
problem Representing and quantifying epistemic uncertainty in machine learning.
method Examined the geometric representation of credal sets as -dimensional polytopes and their volume as a measure of uncertainty.
result The volume of a credal set is a meaningful measure of epistemic uncertainty in binary classification but not in multi-class.
Let N be a complete hyperbolic 3-manifold that is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We show N is homeomorphic to the interior of a compact 3-manifold, or tame, if one of the following conditions holds: (1) N has non-empty conformal boundary, (2) N is not homotopy equivalent to a compres…
Geometric recursionmath.GT
Geometric recursion constructs measurable functions on moduli spaces.
problem Constructing measurable functions on moduli spaces of bordered Riemann surfaces.
method Inductive construction via excisions of pairs of pants, with convergence conditions.
result Geometric recursion produces functions that can be integrated with respect to the Weil-Petersson measure.
New findings on geometric flows and equidistribution in Hilbert geometry.
problem Characterizing dynamical and counting results in Hilbert geometry.
method Study of dynamical and counting results in rank-one properly convex projective structures with Hilbert metrics.
result Hilbert geodesic flow is strongly mixing and orbits and primitive closed geodesics equidistribute.
Spectral convergence in geometric quantization -- the case of non-singular Langrangian fibrationsmath.DG
New approach to geometric quantization for symplectic manifolds.
problem Quantization of symplectic manifolds with non-singular Lagrangian fibrations.
method Using spectral convergence of metric measure spaces, the authors develop a new geometric quantization approach.
result Spectral and quantum Hilbert space convergence results for Kähler and almost Kähler quantizations.
The paper extends the market price of risk for electricity swap contracts, incorporating jump risk.
problem Pricing electricity swap contracts with consideration of jump risk.
method Introducing a Merton type model with jumps and transferring to the physical measure, comparing arithmetic and geometric averaging.
result A decomposition of swap's market price of risk into classical and market price of risk components.
Fisher width is a geometric measure of complexity on statistical manifolds.
problem Complexity measures on statistical manifolds
method Introducing Fisher width as a Fisher-geometric analogue of Gaussian width
result Fisher width retains key structural features of Gaussian width while capturing anisotropic geometric effects
Heat-Kernel Entropy Profiles and Geometric Effective Sample Size for Weighted Measures on Manifoldsstat.ML
New summary measures reveal geometric structure in weighted measures on manifolds.
problem Lack of geometric information in standard weight-only summaries.
method Heat-kernel entropy profiles, tracking nonuniformity across scales.
result Geometric effective sample size discounts nearby or duplicate particles.
Paper solves a geometric problem involving mixtures of area and curvature measures.
problem Investigates a geometric problem involving mixtures of area and curvature measures.
method Establishes a gradient estimate to prove the existence of a solution.
result Proves the existence of an even, smooth, strictly convex solution for .
Brakke flow definitions proven equal.
problem Proving equality of various Brakke flow definitions.
method Corrected proof of Brakke's §3.5 estimate.
result Most Brakke flow definitions are equivalent.
CantorNet tests geometric and topological complexity in neural networks.
problem Understanding self-similar patterns in neural networks.
method Inspired by Cantor set, CantorNet introduces novel complexity measures.
result CantorNet's decision boundaries are analytically known and can be arbitrarily ragged.
Normal-bundle Bootstrapstat.ML
Normal-bundle bootstrap generates new data preserving geometric structure.
problem Probabilistic models often exhibit salient geometric structure.
method NBB method decomposes probability measure into manifold and normal spaces, estimates manifold as density ridge, and generates new data by bootstrapping projection vectors.
result NBB generates new data that preserves the geometric structure of a given data set.
Proves the bending map is proper for hyperbolic 3-manifolds.
problem Properness of the bending map in hyperbolic 3-manifolds.
method Analyzes geometric properties and isotopy classes of homeomorphisms.
result Proving the bending map is proper for hyperbolic 3-manifolds.
Reflected geometric Brownian motion models are not arbitrage-free.
problem No-arbitrage condition violation in financial markets.
method Analysis of reflected geometric Brownian motion models.
result Models violate even the weakest no-arbitrage condition.
Unified theory of measure-preserving diffusions on manifolds.
problem Deriving a complete recipe for measure-preserving diffusions on manifolds.
method Developed a geometric theory that unifies and generalizes previous constructions, relying on intrinsic geometry of the target measure.
result The completeness result is a direct consequence of manifold topology and target measure geometry.
The paper finds a geometric way to minimize a convex function to construct isotropic measures.
problem Constructing isotropic measures in convex bodies.
method Minimizing a convex function in a high-dimensional space.
result Geometric interpretation of the minimizer as a derivative.
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.
New proof of Kondo-Tanaka theorem using geometric measure theory.
problem Existence of special systems of Whitney flat 1-forms on homology manifolds.
method Geometric measure theory and tools from non-smooth analysis.
result Simple new proof of Kondo-Tanaka theorem and its converse.
New formulas for geometric measures in vector spaces.
problem Local additive kinematic formulas for vector spaces.
method Introducing dual area measures and proving their convolution product.
result Local additive kinematic formulas in hermitian vector spaces.
Study shows central limit theorem for counting measures in non-smooth spaces.
problem Counting measures in non-smooth spaces with coarse negative curvature.
method Established central limit theorems for actions of groups on hyperbolic spaces without properness or smoothness assumptions.
result General framework allows for applications in geometrically finite manifolds and intersection numbers.
Deep learning approximates geometric measures of planar curves.
problem Approximating differential invariants of planar curves.
method Utilizing deep neural networks to estimate geometric measures of planar curves.
result Deep neural networks can learn to overcome instabilities and sampling artifacts.
Study extreme values of stable random fields on geometric spaces.
problem Understanding extreme values of stable random fields on various geometric spaces.
method Analyzing extreme values through Patterson-Sullivan measures and extremal cocycle growth.
result Established a dichotomy for the growth-rate of maxima sequences of stable random fields.
New measures found in 3-uniform geometry.
problem Understanding non-flat uniform measures in geometric measure theory.
method Combining combinatorial methods and distance symmetry properties.
result Infinite family of 3-uniform measures constructed.
The paper introduces a new method to measure the shape relations between biological objects using r-parallel sets.
problem The influence of neighboring objects on the shape and function of biological objects.
method The authors develop a theory based on spatial point processes to measure the geometrical interaction between objects.
result The proposed measures provide detailed information about the shape of individual objects and their interactions.
Survey explores geometric aspects of policy optimization in control systems.
problem Understanding the geometric relationships between control design and optimization.
method Geometric perspective on policy optimization, focusing on parameterization and topology.
result Implications of policy geometry on stability and performance of local search algorithms.
Unified geometric scattering model for measure spaces.
problem Improving CNNs for non-Euclidean data.
method Unified geometric scattering model for measure spaces.
result Unified model includes previous work and applies to more general settings.