We observe after Bayle and Rosales that the Levy-Gromov isoperimetric inequality generalizes to convex manifolds with boundary.
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 “Gromov's observation”
New model clusters graphs using Gromov-Wasserstein discrepancy.
problem Graph clustering with topological structures and node attributes.
method Gromov-Wasserstein discrepancy for relational graph comparison; learns atoms and weights via minimization of discrepancy.
result Model achieves flexible factorization of unaligned graphs with different sizes.
Study on 4-manifolds with positive scalar curvature.
problem Characterizing 4-manifolds with positive scalar curvature.
method Geography problem approach focusing on four-dimensional case.
result Survey of mathematical work and strengthening of Carr's result.
The paper proves the Singer conjecture for aspherical complex surfaces and refines Gromov's inequality.
problem Proving the Singer conjecture and refining Gromov's inequality for aspherical complex surfaces.
method Proof of the Singer conjecture for aspherical complex surfaces with residually finite fundamental group, and refinement of Gromov's inequality for non-residually finite surfaces.
result Proof of the Singer conjecture for aspherical complex surfaces with residually finite fundamental group.
In the celebrated book entitled Metric Structures for Riemannian and Non-Riemannian Spaces, so-called Green Book, Gromov presented a problem regarding a metric measure space. Gromov posed the question Bound the expansion coefficient from below in terms of the observable diameter. The overall aim of the current study is…
On fill-ins with scalar curvature bounded from below and an inequality of Hijazi-Montiel-Roldánmath.DG
Researchers prove an inequality linking spin manifold fill-ins to hyperspherical radius.
problem Proving an inequality relating the infimum of mean curvature to hyperspherical radius for spin manifolds.
method Combining Hijazi-Montiel-Roldán inequality and Bär's recent theorem; providing an alternative proof based on Bär-Ballmann work.
result Proved inequality linking spin manifold fill-ins to hyperspherical radius.
We propose a scalable Gromov-Wasserstein learning (S-GWL) method and establish a novel and theoretically-supported paradigm for large-scale graph analysis. The proposed method is based on the fact that Gromov-Wasserstein discrepancy is a pseudometric on graphs. Given two graphs, the optimal transport associated with th…
The measure concentration property of an mm-space is roughly described as that any 1-Lipschitz map on to a metric space is almost close to a constant map. The target space is called the screen. The case of is widely studied in many literature (see \cite{gromov}, \cite{ledoux}, \cite{mil2}…
Thanks to a theorem of Brock on comparison of Weil-Petersson translation distances and hyperbolic volumes of mapping tori for pseudo-Anosovs, we prove that the entropy of a surface automorphism in general has linear bounds in terms of Gromov norm of its mapping torus from below and in bounded geometry case from above. …
Robustly aligns datasets with partial GW distance to handle contamination.
problem Aligning contaminated datasets using Gromov-Wasserstein distances.
method Proposes a partial GW distance estimator to minimize distortion from outliers.
result The partial GW distance estimator is minimax optimal and near-optimal in finite samples.
Study geometric quantization and measured Gromov-Hausdorff convergence of frame bundle metrics.
problem Understanding the convergence of frame bundle metrics and their relation to Gromov-Hausdorff convergence.
method Analyzes the one-parameter family of Riemannian metrics on the frame bundle of a prequantum line bundle, considering the convergence to metric measure spaces with -actions.
result The frame bundle metrics converge to metric measure spaces with -actions, which depend on the choice of base point in Bohr-Sommerfeld fibers.
Paper shows limits of Heisenberg manifolds are flat tori.
problem Understanding limits of sub-Riemannian Heisenberg manifolds.
method Analyzes collapsed Gromov--Hausdorff limits of compact Heisenberg manifolds.
result Collapsed limits are isometric to flat tori.
Improved spectral clustering via Gromov-Wasserstein Learning.
problem Optimizing graph partitioning performance.
method Bridge spectral clustering and GWL, using heat kernel for stable node correspondences.
result Improved graph partitioning results without compromising theoretical guarantees.
We compactify the classical moduli variety of principally polarized abelian varieties of complex dimension by attaching the moduli of flat tori of real dimensions at most in an explicit manner. Equivalently, we explicitly determine the Gromov-Hausdorff limits of principally polarized abelian varieties. Th…
The paper proves Gromov hyperbolicity of certain metrics using isoperimetric inequalities.
problem Investigating Gromov hyperbolicity of specific metrics.
method Using isoperimetric inequalities to characterize Gromov hyperbolicity.
result Characterization of domains where these metrics are Gromov hyperbolic.
We show that the Gromov boundary of the free factor graph for the free group Fn with n>2 generators is the space of equivalence classes of minimal very small indecomposable projective Fn-trees without point stabilizer containing a free factor equipped with a quotient topology. Here two such trees are equivalent if the …
Proof of Gromov's theorem on convex polytopes with acute angles.
problem Gromov's conjecture on extremal scalar curvature of convex polytopes.
method Smoothing construction using Dirac operator techniques.
result Detailed proof of Gromov's theorem.
New theorem using Ricci flow for Gromov almost flat manifolds.
problem Conditions for Gromov almost flat manifolds.
method Employing Ricci flow to derive a new theorem.
result New theorem with weaker condition than Gromov--Ruh Theorem.
Potential theory extended to Gromov hyperbolic spaces.
problem Extending potential theory to a new class of spaces.
method Unified framework for Gromov hyperbolic metric measure spaces.
result Boundary Harnack inequalities and complete classification of positive harmonic functions.
The study proves Gromov hyperbolicity for certain complex domains.
problem Characterizing Gromov hyperbolicity for complex domains.
method Analyzing domains in with finite d'Angelo type and using automorphisms.
result Domains in with finite d'Angelo type are Gromov hyperbolic.
It is well known that quasi-isometric embeddings of Gromov hyperbolic spaces induce topological embeddings of their Gromov boundaries. A more general question is to detect classes of functions between Gromov hyperbolic spaces that induce continuous maps between their Gromov boundaries. In this paper we introduce the cl…
Connectivity proven in large rank Gromov boundary of free factor complex.
problem Connectivity of Gromov boundary in large rank free factor complex.
method Analyzing Gromov boundary and free factor complex properties.
result Gromov boundary is path connected and locally path connected in large rank.
The paper proves stability in compact finite dimensional Alexandrov spaces using equivariant Gromov--Hausdorff convergence.
problem Stability in compact finite dimensional Alexandrov spaces.
method Equivariant Gromov--Hausdorff convergence and almost commutative diagrams.
result Stability result in compact finite dimensional Alexandrov spaces.
Note on the computational complexity of Gromov-Wasserstein distance.
problem Computational difficulty of Gromov-Wasserstein distance.
method Analysis of the optimization problem structure and providing explicit examples.
result Gromov-Wasserstein distance optimization problem is non-convex quadratic.
In 1969 M. Gromov in his PhD thesis greatly generalized Smale-Hirsch-Phillips immersion-submersion theory by proving what is now called the h-principle for invariant open differential relations over open manifolds. Gromov extracted the original geometric idea of Smale and put it to work in the maximal possible generali…
Develop criteria to distinguish Gromov-Thurston manifolds using algebraic Dehn fillings.
problem Distinguishing homotopy types of Gromov-Thurston manifolds
method Using virtual Dehn fillings of relatively hyperbolic groups
result Criteria to distinguish homotopy types
Extends Gromov's theorem with amenable covers.
problem Gromov's Vanishing Theorem limitations.
method Gromov's multicomplex theory, relative bounded cohomology.
result Relative version of Gromov's Vanishing Theorem.
Boundary rigidity defined for hyperbolic spaces, tied to geometric properties.
problem Understanding boundary rigidity in Gromov hyperbolic spaces.
method Analyzing properties of Gromov hyperbolic spaces and their boundaries.
result Boundary rigidity is equivalent to positive Cheeger isoperimetric constant and non-amenability.
Paper proves Gromov's cube inequality in all dimensions.
problem Proving Gromov's cube inequality on scalar curvature in all dimensions.
method Used Dirac operator method to prove cube inequality with optimal constant.
result Proved cube inequality in all dimensions with optimal constant.
Extends Gromov's optimal systolic inequality to manifolds with specific cohomology properties.
problem Finding optimal systolic inequalities for manifolds with complex cohomology structures.
method Extends Gromov's inequality to manifolds with fundamental cohomology classes as cup products of 2-dimensional classes.
result Provides an optimal systolic inequality for a new class of manifolds.
Study of Gaussian distributions using entropic Gromov-Wasserstein and inner product Gromov-Wasserstein.
problem Optimal transportation between Gaussian distributions with different dimensions.
method Entropic Gromov-Wasserstein and inner product Gromov-Wasserstein, with closed-form expressions and von Neumann's trace inequality.
result Closed-form expressions for the entropic IGW and its unbalanced variant between Gaussian distributions.
The paper examines hyperbolicity in bounded strongly minimally convex domains in R^d.
problem Investigating hyperbolicity in bounded strongly minimally convex domains.
method Analyzing the minimal metric and Hilbert metric in convex domains.
result Every bounded strongly minimally convex domain is Gromov hyperbolic.
Researchers describe the Gromov boundary of a graph related to surfaces.
problem Understanding the Gromov boundary of a graph associated with surfaces.
method Described a dense subset of the Gromov boundary as geodesic laminations, proving the graph satisfies a bounded geodesic image theorem.
result The boundary is not compact.
Paper proves Gromov's conjecture on manifolds with certain group properties.
problem Gromov's conjecture on positive scalar curvature and simplicial volume.
method Proves conjecture under a fundamental group decay property.
result Proves Gromov's conjecture for manifolds with a weakened rapid decay property.
Study Gromov-Hausdorff convergence of metric pairs and tuples.
problem Understanding convergence in metric spaces.
method Prove equivalence of definitions, embedding, completeness, and compactness theorems.
result Relative version of Fukaya's theorem and finiteness theorem for stratified spaces.
Two new proofs of Gromov's non-squeezing theorem using curve reparametrization and gradient bounds.
problem Gromov's non-squeezing theorem in symplectic geometry.
method Reparametrization of pseudo-holomorphic curves and application of mean value inequality or Gromov-Schwarz lemma.
result Uniform bounds on the gradient of pseudo-holomorphic curves leading to compactness of moduli space.
In this paper, using the gluing formula of Gromov-Witten invariants under symplectic cutting, due to Li and Ruan, we studied the Gromov-Witten invariants of blow-ups at a smooth point or along a smooth curve. We established some relations between Gromov-Witten invariants of M and its blow-ups at a smooth point or along…
Paper answers Gromov's compactness question on noncompact manifolds.
problem Gromov's compactness question on positive scalar curvature metrics.
method Construct examples and prove vanishing of certain index theoretic invariants.
result Positive answer for a class of 1-tame manifolds.
We prove two tropical gluing formulae for Gromov-Witten invariants of exploded manifolds, useful for calculating Gromov-Witten invariants of a symplectic manifold using a normal-crossing degeneration. The first formula generalizes the symplectic-sum formula for Gromov-Witten invariants. The second formula is stronger, …
Study describes limits of surfaces in a mathematical space.
problem Understanding limits of surfaces in mathematical spaces.
method Completely described Gromov-Hausdorff closure of surfaces.
result Completely described the closure of surfaces.
In this article we exhibit the largest constant in a quadratic isoperimetric inequality which ensures that a geodesic metric space is Gromov hyperbolic. As a particular consequence we obtain that Euclidean space is a borderline case for Gromov hyperbolicity in terms of the isoperimetric function. We prove similar resul…
Proposes a method to align Hawkes processes across different event spaces.
problem Aligning Hawkes processes in multiple event spaces.
method Fused Gromov-Wasserstein alignment for Hawkes processes.
result The method effectively aligns Hawkes processes and their event types.
Shows flexible sheaves as fibrant objects for Gromov's h-principle.
problem Applying the h-principle to partial differential relations.
method Interprets flexible sheaves as fibrant objects in a model structure.
result Flexible sheaves can be understood as fibrant objects.
The paper studies the connectedness of a graph's boundary for surfaces.
problem Understanding the topology of the Gromov boundary of fine curve graphs for surfaces.
method Proved a bounded geodesic image theorem, used to show linear connectivity of the Gromov boundary.
result The Gromov boundary of fine curve graphs for surfaces is linearly connected.
Extends Gromov non-squeezing to locally conformally symplectic structures.
problem Generalizing Gromov non-squeezing to new geometric structures.
method Deformation theory applied to locally conformally symplectic structures.
result Proves a new extension of the Gromov non-squeezing phenomenon.
Enhanced Bishop-Gromov theorem for homogeneous and inhomogeneous spaces.
problem Bounding the volume growth of geodesic balls in spaces.
method Introducing coefficient shuffling and using the Raychaudhuri equation, geodesic flow conservation, and the full spectrum of Ricci curvature.
result Upper bounds on the average rate of growth of geodesics for finite-volume inhomogeneous spaces.
We consider Gromov-Thurston examples of negatively curved n-manifolds which do not admit metrics of constant sectional curvature. We show that for each n some of the Gromov-Thurston manifolds admit strictly convex real-projective structures.
Counterexample disproves key index computation in Gromov's conjecture paper.
problem Disproving an index computation in Gromov's conjecture paper.
method Constructing a counterexample to an index computation.
result Counterexample disproves the main result of the paper.