Proves real analyticity on surfaces based on restrictions.
problem Determining analyticity on non-continuous functions on manifolds.
method Analyzes restrictions to submanifolds homeomorphic to 2-sphere.
result Analyticity on manifold follows from analytic restrictions.
Real analytic submersion images are always real analytic.
problem Analyticity of submersion images
method Analyticity proof for Riemannian submersions
result Image of real analytic submersion is real analytic
Lie group structure on analytic diffeomorphisms of manifolds with corners.
problem Defining a Lie group structure on diffeomorphisms of manifolds with corners.
method Developed a new construction for manifolds with corners.
result Smooth Lie group structure on real analytic diffeomorphisms of compact manifolds with corners.
We begin by showing that every real analytic orbifold has a real analytic Riemannian metric. It follows that every reduced real analytic orbifold can be expressed as a quotient of a real analytic manifold by a real analytic almost free action of a compact Lie group. We then extend a well-known result of Nomizu and Ozek…
Analytic knots have lower 4-ball genus bounds.
problem Understanding the 4-ball genus of analytic knots and links.
method Sharp lower bounds for 4-ball genus of analytic links contained in a tubular neighborhood of smoothly analytic knots.
result Sharp lower bounds for the 4-ball genus of analytic links.
Survey shows degenerate elliptic equations have analytic properties despite low regularity.
problem Understanding analytic properties of degenerate elliptic equations.
method Explains why solutions of a specific degenerate elliptic equation are analytic.
result Solutions of a specific degenerate elliptic equation are analytic despite low regularity.
Analytic curves and submanifolds classified based on symmetry.
problem Classifying analytic curves and submanifolds based on symmetry.
method Analytic curves and submanifolds classified based on symmetry under Lie group action.
result Analytic curves and submanifolds are either exponential or decomposable into symmetry-free subcurves.
We construct an infinite dimensional real analytic manifold structure for the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known the constructio…
Inspired by the work of Boris Vertman on refined analytic torsion for manifolds with boundary, in this paper we extend the construction of the Cappell-Miller analytic torsion to manifolds with boundary. We also compare it with the refined analytic torsion on manifolds with boundary. As a byproduct of the gluing formula…
Analytic 1-submanifolds decompose into symmetry-free segments.
problem Classifying symmetry of analytic 1-submanifolds.
method Discretely generating free segments via Lie group action.
result Free analytic 1-submanifolds decompose into countably many symmetry-free segments.
The paper defines wave-front singularities using explicit analytic functions.
problem Characterizing the images of wave-front singularities.
method Explicit resultant computations to construct main-analytic functions.
result Explicit formulas for main-analytic functions of wave-front singularities of types A, D, and E.
Analytic completeness criterion applied to constant mean curvature surfaces.
problem Determining the analytic completeness of constant mean curvature surfaces.
method Defining arc-properness and applying it to surfaces in de Sitter 3-space.
result A criterion for the analytic completeness of G-catenoids and their extensions.
Transforms uniquely determine Higgs fields on real-analytic manifolds.
problem Determining Higgs fields from transforms on manifolds.
method Matrix-weighted real-analytic double fibration transforms.
result Higgs fields can be uniquely determined from transforms.
Analytic linearization and holomorphic extensions for proper groupoids.
problem Analytic linearization and holomorphic extensions of proper groupoids.
method Establish analytic linearization around invariant submanifolds and apply to holomorphic extensions.
result Proper groupoids admit holomorphic extensions.
In this paper we show that the Ray-Singer complex analytic torsion is trivial for even dimensional Calabi-Yau manifolds. Then we define the quaternionic analytic torsion for quaternionic manifolds and prove that they are metric independent. In dimension four, the quaternionic analytic torsion equals to the self-dual an…
Proves an analytic Bertini theorem, generalizing previous work.
problem Generalizing previous results in algebraic geometry.
method Analytic Bertini theorem proof.
result Generalizes previous results in algebraic geometry.
Paper compares absolute and relative real analytic torsion forms over fibrations.
problem Analytic torsion forms over fibrations with boundaries.
method Gluing formula of analytic torsion forms proved by M. Puchol, Y. Zhang, and the author.
result Establishes a comparison formula of absolute and relative real analytic torsion forms.
Proper Lie groupoids have real analytic structures.
problem Finding analytic structures for proper Lie groupoids.
method Demonstrating the existence of a compatible real analytic structure.
result Proper Lie groupoids have real analytic structures.
Validates replica trick for simple models using replica analytic continuation.
problem Validating replica trick for complex systems.
method Applying replica analysis to simple models, focusing on replica analytic continuation.
result Replica analytic continuation is a robust procedure in replica analysis.
Analytic metrics are uniquely determined by their scattering map.
problem Determining Riemannian manifolds from scattering data.
method Analytic negatively curved Riemannian manifolds with strictly convex boundary.
result The scattering map determines the manifold up to isometry.
This report synthesizes research advances in integrating machine learning with visual analytics.
problem Underexplored combination of machine learning and data visualization in visual analytics.
method Synthesizing research advances to highlight the progress and challenges.
result Opportunities and challenges identified for future research in machine learning and visual analytics.
Proves a local analytic Bertini theorem confirming a conjecture.
problem Analytic Bertini theorem in local generality.
method Full generality proof of the local analytic Bertini theorem.
result Confirms a conjecture by Boucksom in local analytic settings.
Ancient solutions to heat equations on graphs are shown to be analytic in time.
problem Analyzing the analyticity of ancient solutions to heat equations on graphs.
method Proving time analyticity under a sharp growth condition.
result Ancient solutions to heat equations on graphs are time analytic under certain conditions.
Analytic torsion defined for non-compact Lie groups and discrete subgroups.
problem Defining and calculating analytic torsion for non-compact Lie groups and their discrete subgroups.
method Localised analytic torsion and relative analytic torsion defined for Lie groups of type I, using representations and discrete subgroups.
result Relative analytic torsion of (G,Γ) coincides with Lott L2 analytic torsion of a covering space. Analytic Kähler potentials yield analytic Bergman kernels.
problem Characterizing Bergman kernels for analytic Kähler potentials.
method Linear recursive formula for Bergman kernel coefficients, simplified from Charles's work.
result Bergman kernels are analytic symbols with phase determined by Kähler potential polarization.
Paper generalizes a theorem for real analytic singularities.
problem No specific problem stated; focuses on generalization.
method Generalization of a theorem for complex singularities.
result Generalized Join theorem for real analytic singularities.
Defines hypercomplex analytic spaces and schemes.
problem No specific problem stated; focuses on definitions.
method Definitions and quotient construction.
result Canonical association of hypercomplex spaces to quotients.
Deep neural nets converge exponentially fast for analytic functions.
problem Analytic function approximation in low dimensions.
method Exponential convergence rate of deep neural networks for analytic functions.
result Deep neural nets achieve exponential convergence for analytic functions.
Analytic torsion studied for fibred boundary metrics, with applications to conic degeneration.
problem Analytic torsion of fibred boundary metrics and conic degeneration.
method Established invariance and gluing formula for renormalized analytic torsion under deformations of metrics.
result Recovery of a result by Sher and Guillarmou about analytic torsion under conic degeneration.
Analytic proof solves differential geometry problem.
problem Solving the system of equations ∣ablau∣=f(u), Δu=g(u) in connected domains. method Analytic approach to solve differential equations.
result Validated Segre's Theorem in differential geometry.
Analytic torsions on contact spheres are calculated using Rumin complex.
problem Calculating analytic torsions for contact spheres.
method Explicitly wrote down eigenvalues of Rumin Laplacian and expressed analytic torsion functions in terms of Riemann zeta function.
result Functions of analytic torsions vanish at the origin and were determined.
Study the asymptotic behavior of analytic torsion for hyperbolic orbifolds.
problem Understanding the asymptotic behavior of analytic torsion for hyperbolic orbifolds.
method Analyzing sequences of representations associated to rays of highest weights.
result Asymptotic behavior of analytic torsion for hyperbolic orbifolds is understood.
A new method for non-rigid point set registration reduces computational complexity.
problem Efficiently registering non-rigid point sets with large numbers of points.
method Structured Analytic Coherent Point Drift (Analytic-CPD) reformulates CPD for structured analytic mappings.
result Analytic-CPD reduces computational complexity by controlling the deformation model's dimensionality.
Analytic torsion matches Ray-Singer for specific nilmanifolds.
problem Matching analytic torsion with Ray-Singer in specific nilmanifolds.
method Examined rank two distributions on 5D nilmanifolds, proving torsion equality.
result Analytic torsion equals Ray-Singer torsion in these specific nilmanifolds.
We define analytic torsion of Z_2-graded elliptic complexes as an element in the graded determinant line of the cohomology of the complex, generalizing most of the variants of Ray-Singer analytic torsion in the literature. It applies to a myriad of new examples, including flat superconnection complexes, twisted analyti…
Analytic sub-Riemannian geodesics in 3D are always C1 and analytic except finitely many points.
problem Regularity of sub-Riemannian minimizing geodesics in 3D analytic manifolds.
method Investigation of totally nonholonomic analytic distributions, proof of Hausdorff dimension, and regularity of minimizing geodesics.
result Minimizing sub-Riemannian geodesics in 3D analytic manifolds are C1 and analytic except finitely many points.
Ancient solutions of heat equation with exponential growth are analytic in time.
problem Analyticity of solutions to the heat equation in time.
method Proving analyticity for ancient solutions with exponential growth.
result Ancient solutions with exponential growth are analytic in time.
We prove the existence of a local analytic Levi decomposition for analytic Poisson structures and Lie algebroids.
Smooth rigid spherical hypersurfaces in C^2 are real analytic.
problem Classifying smooth rigid spherical hypersurfaces in C^2.
method Proving real-analyticity through smoothness.
result Every smooth rigid spherical hypersurface in C^2 is real analytic.
Study Cowen-Douglas operators from analytic function spaces.
problem Analytic continuation and spectrum of Cowen-Douglas operators.
method Investigate Banach spaces of analytic functions and their operators.
result Analytic continuations of functions relate to the spectrum of Cowen-Douglas operators.
Develops a semi-analytic method for auto-callable accrual notes valuation.
problem Valuation of auto-callable structures with accrual features subject to barrier conditions.
method Extends recent studies of multi-assessed binaries to time-dependent parameters, using a semi-analytic approach.
result The semi-analytic approach is more advantageous for high precision valuation compared to Monte Carlo methods.
The article examines twisted cohomologies on algebraic and analytic varieties.
problem Understanding and comparing twisted cohomologies on algebraic and analytic varieties.
method Comparison and definition of twisting parameters in both categories, algebraic and analytic.
result Reviewed isomorphisms of twisted cohomologies for cohomologous twisting parameters.
The book explores analytic properties of groups and their actions.
problem Analytic properties of groups and their actions.
method Analytic approaches to studying groups and their actions, focusing on amenability and Kazhdan's property (T).
result Introduction of useful tricks, ideas, and lemmas in Analytic Group Theory.
Geometric analysis on real analytic manifolds using seminorms.
problem Characterizing operations on real analytic manifolds and vector bundles.
method Using seminorms and geometric decompositions of jet bundles.
result New characterizations of real analytic mappings and operations.
Support theorems for light ray transforms on analytic manifolds.
problem Understanding functions on Lorentzian manifolds via lightlike geodesics.
method Analyticity of manifold and weight, support theorems for ray transforms.
result Support theorems for integrating functions on analytic Lorentzian manifolds.
Simplified proof of gluing formula for analytic torsion forms.
problem Proving the gluing formula for analytic torsion forms.
method Extending prior work to the family case, presenting a new proof.
result Simplified proof of the gluing formula.
Analytic surgery and gluing formula for torsion forms in fiber bundles.
problem Behavior of torsion forms under analytic surgery in fiber bundles.
method Analytic surgery and gluing formula for Bismut-Lott torsion and eta forms.
result Gluing formula for Bismut-Lott analytic torsion and eta forms under surgery limit.
Analytic networks with bounded coefficients can't outperform polynomial approximations.
problem Approximation limits of neural networks with analytic activation functions under coefficient constraints.
method Deterministic analysis using comparison argument and Bernstein-type estimates.
result Networks with analytic activation functions and controlled coefficients cannot outperform classical polynomial approximation rates on non-analytic targets.