Study geometric bounds on generalized Ricci flow.
problem No specific problem stated; focuses on bounds.
method Analogous geometric quantities and bounds proven.
result Geometric and analytic bounds established.
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48 results for “geometric bounding”
The figure-eight knot's complement bounds a hyperbolic 4-manifold.
problem Bounding hyperbolic knot complements in higher dimensions.
method Embedding tessellated 3-manifolds in 4-manifolds.
result The figure-eight knot's complement geometrically bounds a hyperbolic 4-manifold.
New geometric SDEs and discretizations on Riemannian manifolds with error bounds.
problem Modeling diffusion processes on Riemannian manifolds with geometric SDEs.
method Introduced a new construction of geometric SDEs and provided non-asymptotic error bounds.
result First non-asymptotic error bound for geometric Euler-Murayama discretization.
New findings show some hyperbolic 3-manifolds can't be geometrically bounded.
problem Understanding which cusped hyperbolic 3-manifolds can be geometrically bounded.
method Analyzing embeddings and geometric properties of hyperbolic 3-manifolds.
result Some cusped hyperbolic 3-manifolds cannot be geometrically bounded.
New bounds for prediction with experts using geometric stopping.
problem Online prediction with expert advice, focusing on geometric stopping.
method Potential-based framework, explicit bounds construction.
result First explicit lower and upper bounds in geometric stopping setting.
Paper finds new 3D shapes that can be inside a 4D space.
problem Finding new 3D shapes with specific properties.
method Examined arithmetic hyperbolic 3-manifolds and their homology.
result Discovered infinitely many 3D shapes that are rational homology spheres and can bound geometrically.
Algorithm checks if geometrically triangulated manifolds are isometric.
problem Determining if two geometric triangulations of manifolds are isometric.
method Sequence of Pachner moves and barycentric subdivisions with bounds on lengths.
result Bounding the length of transformations between triangulations.
New math shows many 3D hyperbolic shapes can fit together.
problem Counting specific 3D shapes that fit together.
method Examined both arithmetic and non-arithmetic shapes, focusing on their volume.
result The number of such shapes grows super-exponentially with volume.
Lower bounds for Hodge-Laplacian spectrum on orbifolds.
problem Finding bounds for the essential spectrum of Hodge-Laplacian.
method Deriving lower bounds for the essential spectrum of the Hodge-Laplacian on geometrically finite orbifolds and their suborbifolds.
result Lower bounds for the essential spectrum of the Hodge-Laplacian.
New bound on neural network generalization error using geometric complexity.
problem Understanding the generalization capabilities of deep neural networks.
method Derive a new upper bound on generalization error using margin-normalized geometric complexity.
result Empirical validation of the bound for ResNet-18 on CIFAR-10 and CIFAR-100 datasets.
A finite-volume hyperbolic 3-manifold geometrically bounds if it is the geodesic boundary of a finite-volume hyperbolic 4-manifold. We construct here an example of non-compact, finite-volume hyperbolic 3-manifold that geometrically bounds. The 3-manifold is the complement of a link with eight components, and its volume…
Abstract: Geometrically reformulates estimation theory for finite-dimensional C*-algebras.
problem Estimation theory for finite-dimensional C*-algebras.
method Geometrical formulation of estimation theory.
result Derivation of Cramer-Rao and Helstrom bounds.
Study wall singularities in spaces with upper curvature bounds.
problem Understanding singularities in spaces with curvature constraints.
method Geometric structure theorem and geometric characterization for codimension one and two.
result Necessary and sufficient conditions for singular sets to be of codimension at least two.
The paper proves geometric bordisms for specific hyperbolic surfaces.
problem Proving geometric bordisms for Accola-Maclachlan, Kulkarni, and Wiman surfaces.
method Explicit geodesic embeddings and geometric proofs for specific surfaces.
result The surfaces bound geometrically compact hyperbolic 3-manifolds.
Paper provides a lower bound for isoperimetric deficit.
problem Finding a lower bound for isoperimetric deficit.
method Bonnesen-style inequality and geometrical invariants.
result Lower bound for isoperimetric deficit.
We establish a lower bound on the complexity orientable locally orientable geometric 3-orbifolds in terms of Delzant's T-invariants of their orbifold-fundamental groups, generalizing previously known bounds for complexity of 3-manifolds.
The paper classifies group-actions on surfaces of small genus, focusing on bounding and geometrically bounding cases.
problem Classifying group-actions on surfaces of small genus, particularly focusing on bounding and geometrically bounding cases.
method Analyzing large group-actions on surfaces of genus 3, distinguishing between bounding and geometrically bounding cases.
result Identifies which large group-actions on surfaces of genus 3 are bounding or geometrically bounding.
The paper explores symplectic foliations and their leaves on manifolds.
problem Which manifolds can be realized as leaves of codimension-1 symplectic foliations?
method Observations and deformations of symplectic structures; examples of manifolds.
result Examples of manifolds that can be realized as leaves but not as symplectic leaves.
Study eigenvalues on quaternion-Kähler manifolds with geometric bounds.
problem Estimating eigenvalues on quaternion-Kähler manifolds.
method Lower bounds derived from modulus of continuity estimates for heat equation solutions and Laplace comparison theorem.
result Established bounds for first nonzero eigenvalues in terms of dimension, diameter, and scalar curvature.
Sharp bounds on eigenfunctions of the Ornstein-Uhlenbeck operator.
problem Understanding growth rates of eigenfunctions.
method Proving sharp bounds up to lower order terms.
result Sharp bounds for eigenfunctions growth rates.
New invariant for hyperbolic surfaces, geometric criterion for domains.
problem Geometric criterion for bounded domains in complex plane.
method Renormalized volume type invariant on hyperbolic surfaces.
result New geometric criterion for bounded domains in complex plane.
Optimal geometric estimates for Kähler manifolds with bounded Nash entropy
problem Optimal geometric estimates for compact Kähler manifolds
method Proving Sobolev-type inequality and local volume noncollapsing with optimal exponents
result Uniformly bounded -Nash entropy
Novel relations in bounded cohomology of surface groups explained.
problem Exploring linear dependences in bounded cohomology of surface groups.
method Quasi-isometric representations and bounded fundamental classes.
result Linear dependences between geometric bounded classes described.
Geometric finiteness theory for essential surfaces in knot exteriors with geometric bounds.
problem Understanding the topology of essential surfaces in knot exteriors with geometric constraints.
method Developed a relative geometric finiteness theory using bounded geometry and thickness conditions.
result Every bounded-geometry slice contains only finitely many pair-isotopy classes, and topology is recoverable from finite geometric data.
The paper finds rare geometrically bounding hyperbolic 3-manifolds.
problem Bounding hyperbolic 3-manifolds with specific Betti numbers and volumes.
method Constructing hyperbolic 3-manifolds using small cover theory over linearly-glued dodecahedra.
result Constructs closed hyperbolic 3-manifolds with specific Betti numbers and volumes that are geometrically bounding.
Explicit bounds on group size for certain geometric actions.
problem Bounding group size in geometric actions with bounded entropy.
method Proving an explicit function F(k, E) for groups with k-acylindrical splittings.
result Groups with bounded entropy have a finite size bound.
Proves upper bounds for heat kernels evolving on manifolds.
problem Bounding heat kernels on evolving manifolds.
method Logarithmic Sobolev inequalities and ultracontractivity estimates.
result Gaussian upper bounds for heat kernels are derived.
New bounds for geometric flows of Hermitian metrics established.
problem Regularity of geometric flows of Hermitian metrics.
method Establishing a a priori bound for smooth curves of Hermitian metrics.
result New regularity result for Hermitian curvature flows, including the second Chern-Ricci flow.
The paper bounds Pachner moves and systoles in hyperbolic 3-manifolds.
problem Bounding Pachner moves and systoles in cusped hyperbolic 3-manifolds.
method Using geometric ideal triangulations and dihedral angles, the paper gives bounds on Pachner moves and systoles.
result Lower bounds on systole length and Pachner move sequence length.
Geometric tempering fails for Langevin dynamics, proving convergence limits.
problem Proving convergence and limitations of geometric tempering for Langevin dynamics.
method Theoretical investigation of geometric tempering using Langevin dynamics.
result Geometric tempering can lead to exponential time convergence and poor functional inequalities.
Bootstrap bounds on Einstein manifolds using semidefinite programming.
problem Bounding geometric data of closed Einstein manifolds.
method Semidefinite programming applied to consistency conditions of geometric data.
result Bootstrap bounds translate to constraints on Kaluza-Klein modes.
Study geometric structures in transfer learning to avoid negative transfer.
problem Understanding information-theoretic limits of transfer learning without exploiting domain geometry.
method Integrates geometric structure into linear regression models, using Gram matrices of source and target domains.
result Proposes an interpolation estimator that matches minimax lower bound and outperforms existing methods.
The paper shows bounds for a geometric flow related to Type IIB string theory.
problem Establishing derivative bounds for a geometric flow in non-Kähler geometry.
method Unified formulation of the flow with Ricci flow, proving bounds from metric and torsion 1-form uniform bounds.
result Derivative bounds follow from uniform metric and torsion 1-form bounds.
The paper examines torsional rigidity bounds under geometric flows.
problem Torsional rigidity behavior under geometric flows.
method Bounds on torsional rigidity derived under Ricci Flow and Inverse Mean Curvature Flow.
result Inequalities of comparison with the flat disk for torsional rigidity.
Abstract: Overview of scalar curvature constraints in Riemannian spaces.
problem Geometric constraints on Riemannian spaces with lower scalar curvature bounds.
method Exposition of known and new constraints.
result Presentation of geometric constraints implied by scalar curvature bounds.
Estimates mean curvature flow with geometric bounds.
problem Controlling mean curvature flow dynamics.
method Pointwise estimate using initial geometry and jHAj bound.
result Extension theorem and blowup rate estimate of HA.
Optimal bounds for Laplacian eigenvalues on weighted graphs.
problem Finding lower bounds for Laplacian eigenvalues in weighted graphs.
method Formulating bounds in terms of graph geometry, specifically inradius of subsets.
result Optimal lower bounds for the first non-zero eigenvalue in finite volume and Dirichlet Laplacian on subsets with geometric conditions.
Uniform Sobolev, interpolation and geometric Calderón-Zygmund inequalities for graph hypersurfacesmath.DG
The study shows that close hypersurfaces have uniformly bounded inequalities.
problem Bounding inequalities for close hypersurfaces.
method Analyzing families of smooth hypersurfaces close to a fixed one.
result Uniformly bounded constants in Sobolev, Gagliardo-Nirenberg, and geometric Calderón-Zygmund inequalities.
Study sets lower bounds for Kähler manifolds' Laplacian eigenvalues.
problem Finding bounds for eigenvalues on Kähler manifolds.
method Establishes lower bounds using geometric data like dimension, diameter, and curvature.
result Proves bounds for Laplacian eigenvalues on Kähler manifolds.
Constructs geometric decompositions for thick hyperbolic 3-manifolds with bounded rank.
problem Understanding the structure of thick hyperbolic 3-manifolds with bounded rank.
method Geometric decomposition of the convex core of M.
result Upper bounds on Heegaard genus and radius of embedded balls in terms of rank and injectivity radius.
Study on metrics on non-geometric 3-manifolds with rigid topological properties.
problem Characterize metrics on non-geometric 3-manifolds.
method Prove lower bounds for systole and volume, deduce local topological rigidity.
result Closed, irreducible manifolds in the class are diffeomorphic if close enough.
This paper explores and ties together three themes. The first is to establish regularity of a metric tensor, on a manifold with boundary, on which there are given Ricci curvature bounds, on the manifold and its boundary, and a Lipschitz bound on the mean curvature of the boundary. The second is to establish geometric c…
Last SGD iterate bounds for overparameterized linear regression.
problem Analyzing the last iterate risk bounds of SGD with decaying stepsize for overparameterized linear regression.
method Problem-dependent analysis of last iterate risk bounds of SGD with geometrically decaying stepsize.
result Proved nearly matching upper and lower bounds on the excess risk for last iterate SGD with geometrically decaying stepsize.
The study provides criteria for solving the Dirichlet problem at infinity on Cartan-Hadamard surfaces.
problem Solvability of the Dirichlet problem at infinity on Cartan-Hadamard surfaces.
method General criterion and upper radial curvature bounds.
result Solvability of the Dirichlet problem at infinity implies a natural continuous surjection of the Martin boundary onto the geometric boundary.
New method reduces model selection sample complexity for geometric graphs.
problem Model selection in Gaussian Markov fields with sample deficiency.
method Introducing spatial stationarity to geometric graphs, developing information-theoretic bounds and efficient reconstruction techniques.
result Spatial stationarity leads to significant reduction in sample complexity for consistent recovery.
In this paper we prove two results, one semi-historical and the other new. The semi-historical result, which goes back to Thurston and Riley, is that the geometrization theorem implies that there is an algorithm for the homeomorphism problem for closed, oriented, triangulated 3-manifolds. We give a self-contained proof…
We show that a Laplace isospectral family of two dimensional Riemannian orbifolds, sharing a lower bound on sectional curvature, contains orbifolds of only a finite number of orbifold category diffeomorphism types. We also show that orbifolds of only finitely many orbifold diffeomorphism types may arise in any collecti…
This note bounds Courant-sharp eigenvalues using geometric invariants.
problem Bounding Courant-sharp eigenvalues using geometric invariants.
method Determining an upper bound for Courant-sharp eigenvalues in terms of simple geometric invariants.
result An upper bound for Courant-sharp eigenvalues is derived.