New complexity notion connects finite decomposition and asymptotic property C.
problem Understanding and connecting different properties in metric spaces.
method Introducing finite APC-decomposition complexity and proving its implications.
result Finite APC-decomposition complexity implies property A for metric spaces.
Abstract: Formalizes metric spaces with coarse properties, generalizing finite decomposition complexity.
problem Understanding metric spaces with coarse properties.
method Formalizing and generalizing finite decomposition complexity.
result Determines sufficient conditions for metric spaces to satisfy Property A.
Examines properties of holomorphic fibrations in complex geometry.
problem Holomorphic fibrations in complex geometry.
method Analyzes properties of holomorphic fibrations.
result Provides insights into the structure of holomorphic fibrations.
Study the boundary operator property on simplicial complexes, proving essential properties for Hodge theory.
problem Characterize the boundary operator property ∂∂=0 on simplicial complexes. method Characterization in ℓ2 terms of recurrence of links, defining relative cohomology, and proving harmonic eigenforms. result Essential properties for Hodge theory, including weak decomposition and existence of harmonic eigenforms.
Study cohomological and metric properties of non-Kähler complex manifolds.
problem Understanding cohomological invariants and metrics of non-Kähler complex manifolds.
method Partial account of problems through cohomological and metric properties.
result Partial insights into cohomological and metric properties of non-Kähler manifolds.
The paper proves extension theorems for various geometric properties of groups.
problem Various geometric properties of groups and their extensions.
method Proving extension theorems for asymptotic property C, finite decomposition complexity, and strict finite decomposition complexity.
result Groups with certain properties inherit weaker geometric properties.
A property, or statistical functional, is said to be elicitable if it minimizes expected loss for some loss function. The study of which properties are elicitable sheds light on the capabilities and limitations of point estimation and empirical risk minimization. While recent work asks which properties are elicitable, …
Defines coarse versions of property C and decomposition complexity.
problem Tackles coarse versions of property C and decomposition complexity.
method Uses coarse spaces to define coarse versions of asymptotic property C and decomposition complexity.
result Proves coarse property C implies coarse property A and shares features with metric analogs.
Defines relative $\dbar$-complex and studies its curvature properties.
problem Curvature properties of relative $\dbar$-complex and associated vector bundles.
method Definition and study of curvature properties of the relative $\dbar$-complex and associated vector bundles.
result Yamaguchi's theory on subharmonicity of the Green operator can be seen as a curvature property of the quotient bundle.
Machine learning and complexity-entropy methods estimate liquid crystal properties from textures.
problem Extracting physical properties from liquid crystal textures.
method Combining permutation entropy, statistical complexity, and machine learning.
result Significant precision in predicting physical properties of liquid crystals.
Study 2-complexes' homology properties and torsion growth.
problem Quantitative connections between 1-cycle filling inequalities and homology complexities.
method Geometric lower bounds on first homology of finite covers.
result Geometric lower bound on first homology size of finite covers.
Uniform Jordan property proven for Lie groups and complex space transformations.
problem Proving Jordan property for Lie groups and complex space transformations.
method Analyzing families of Lie groups and using algebraic groups properties.
result Uniform Jordan property established for Lie groups and complex space transformations.
Classifies pro-p PD2 pairs and builds a pro-p curve complex.
problem Classifying pro-p Poincaré duality pairs in dimension two. method Using classification of pro-p PD2 pairs to build a pro-p curve complex. result Established basic properties of the pro-p curve complex. Study shows some complex shapes don't fit a certain property.
problem Some aspherical manifolds lack the Bounded Index Property (BIP).
method Analyzes specific aspherical manifolds to prove they don't have BIP.
result Proves existence of aspherical manifolds without BIP.
Derives properties of heat kernel for Rumin complex on Heisenberg groups.
problem Analyzing heat kernel properties for Rumin complex.
method Derives properties of heat equation with Hodge operator on Heisenberg groups.
result Constructs Calderón reproducing formula using heat kernel for Rumin forms.
Introduces regular finite decomposition complexity for metric families.
problem Metric families with finite asymptotic dimension.
method Introduces regular finite decomposition complexity (RFDC) and shows it implies finite decomposition complexity (FDC).
result RFDC has permanence properties including Finite Quotient Permanence.
This paper proves a conjecture about Kähler manifolds and complex space forms.
problem Proving Kähler manifolds satisfying the Δ-property are complex space forms.
method Analyzing Kähler Laplacian and complex Euclidean Laplacian properties.
result Validates the conjecture that Kähler manifolds satisfying the Δ-property are complex space forms.
The paper studies complex space forms via Laplace operators and curvature properties.
problem Characterizing \K manifolds with specific Laplace operator properties.
method Analyzing \K manifolds satisfying the Δ-property and proving curvature implications.
result Complex space forms are characterized by the Δ-property and curvature parallelism.
Study on descent properties of complex affine surfaces under proper morphisms.
problem Understanding descent behavior of homotopy-theoretic properties of smooth affine surfaces.
method Examined Eilenberg-MacLane property and introduced finite homotopy rank-sum property. Proved descent under proper morphisms for surfaces of log Kodaira dimension ≤0.
result Finite homotopy rank-sum property descends under proper morphisms for smooth affine surfaces of log Kodaira dimension ≤0.
We consider different levels of complexity which are observed in the empirical investigation of financial time series. We discuss recent empirical and theoretical work showing that statistical properties of financial time series are rather complex under several ways. Specifically, they are complex with respect to their…
Paper offers a framework for estimating symmetric properties efficiently.
problem Estimating symmetric properties of distributions from samples.
method General framework using profile maximum likelihood (PML) distribution.
result Optimal sample complexity for many properties, practical algorithms.
Study functionals on almost complex structures for Yau's Challenge.
problem Yau's Challenge on compact C-manifolds. method Variational properties of functionals on almost complex structures.
result Variational properties could be used to tackle Yau's Challenge.
Study on complex spaces and their properties.
problem Characterizing relative properties of complex spaces.
method Analyzing indefinite Euclidean and non-flat complex spaces.
result Indefinite Euclidean complex space is not a relative of an indefinite non-flat complex space form.
Groups with special properties always have fixed points.
problem Groups acting on finite CW-complexes without fixed points.
method Exhibited specific groups with strong fixed-point properties.
result Groups with finite generation and torsion-freeness have global fixed points.
Proves a vanishing property for symplectic manifold cohomology.
problem Generalizing complex geometry results to symplectic geometry.
method Based on Tseng and Zhou's vanishing property under symplectic flatness.
result Establishes necessity of symplectic flatness for certain results.
Study on multicalibration for multiple properties, establishing sample complexity bounds.
problem Ensuring unbiasedness across multiple related properties in predictions.
method Establishing upper and lower bounds on sample complexity for multicalibration of multiple properties.
result Matching upper and lower bounds on sample complexity for multicalibration of k properties. The Thurston spine's properties are studied in relation to Morse-Smale complexes.
problem Understanding the Thurston spine's local properties and their global implications.
method Analyzes the Thurston spine as a subset of Teichmüller space and studies its local properties in relation to the systole function.
result The Thurston spine satisfies properties analogous to Morse-Smale complexes, demonstrating its topological significance.
Study on curvature properties and Shafarevich conjecture for complex hyperbolic manifolds.
problem Existence and nonexistence of Kähler metrics with nonpositive curvature on toroidal compactifications.
method Analysis of toroidal compactifications of finite volume complex hyperbolic manifolds, verification of Shafarevich conjecture.
result Verification of Shafarevich conjecture for compactifications of quotients of complex hyperbolic space by non-uniform arithmetic lattices.
While small deformations of Kähler manifolds are Kähler too, we prove that the cohomological property to be C∞-pure-and-full is not a stable condition under small deformations. This property, that has been recently introduced and studied by T.-J. Li and W. Zhang in [Comparing tamed and compatible symp…
Research examines properties of special metrics on complex manifolds.
problem Properties of Hermitian metrics with proportional curvature traces.
method Study of basic properties and examples of Chern-Einstein metrics.
result Examples of Chern-Einstein metrics are provided.
Let (M,g) be a Riemannian 4-manifold. The twistor space Z->M is a CP1-bundle whose total space Z admits a natural metric h. The aim of this article is to study properties of complex structures on (Z,h) which are compatible with the CP1-fibration and the metric h. The results obtained enable us to translate some metric …
The study defines and explores properties of complex Sasakian manifolds.
problem Understanding the geometric structure of complex Sasakian manifolds.
method Definition and analysis of properties, curvature relations, and flatness conditions.
result Obtained useful curvature relations and examined flatness conditions for general curvature tensor B.
Research preserves coarse property C and related dimensions through direct products.
problem Preserving properties in coarse geometry through direct products.
method Demonstrates preservation of coarse property C and related dimensions through finite coarse direct products.
result Coarse property C and related dimensions are preserved by direct products.
Complex captures group properties, invariant under quasi-isometry.
problem Classical properties of subgroups in a group pair.
method Introduces coset intersection complex to study group properties.
result Quasi-isometry invariance of coset intersection complex.
Study complex properties of minimal Lagrangian submanifolds in Kaehler spaces.
problem Complex properties of minimal Lagrangian submanifolds in Kaehler spaces.
method Mix of holomorphic curve techniques and convexity results.
result Minimal Lagrangians do not admit fillings by holomorphic discs in negative curvature case.
The paper characterizes and studies compact subsets of complex projective space with specific line intersection properties.
problem Characterizing compact subsets of complex projective space with specific line intersection properties.
method Characterization and study of compact subsets of complex projective space with line intersection properties.
result Characterization of quadratic R-algebraic subsets of complex projective space.
Unified method for estimating properties of large domain distributions efficiently.
problem Estimating properties of distributions over large domains efficiently.
method Piecewise-polynomial approximation technique for constructing sample- and time-efficient estimators.
result Near-linear-time computable estimators with optimal and highly-concentrated approximation values.
An additional minimal simplicial n-complex contains a non-splittable link in R^(2n).
problem Constructing minimal simplicial n-complexes with a specific link property.
method Presenting a new minimal simplicial n-complex.
result An additional simplicial n-complex with the same link property.
The paper studies complex Finsler metrics on complex Lie groups.
problem Characterizing properties of left invariant complex Finsler metrics on complex Lie groups.
method Using invariant frames, the paper proves properties of the metric and its spray.
result The strongly Kähler, Kähler, and weakly Kähler properties are equivalent for the metric.
Study on positivity properties of vector bundle Monge-Ampère equation.
problem Analyzing positivity in vector bundle Monge-Ampère equation.
method Investigates MA-positivity and MA-semi-positive solutions for different ranks of holomorphic bundles over complex surfaces and manifolds.
result Positivity preservation in rank-two holomorphic bundles but not in higher ranks.
Study cohomological properties of complex manifolds, extending a result to higher dimensions.
problem Upper bound for Bott-Chern cohomology in terms of Betti numbers for compact complex surfaces.
method Suitable metric conditions, extending a result by A. Teleman to higher dimensions.
result Upper bound for Bott-Chern cohomology in terms of Betti numbers for compact complex manifolds.
Paper develops new methods for binary classification with complex performance measures.
problem Complex performance measures in binary classification are not decomposable and require new theoretical and methodological developments.
method Identifies Karmic and threshold-quasi-concavity properties, and develops a computationally practical plug-in classifier.
result Bayes optimal classifier is a threshold function of conditional probability, leading to practical classification error analysis.
We introduce certain homology and cohomology subgroups for any almost complex structure and study their pureness, fullness and duality properties. Motivated by a question of Donaldson, we use these groups to relate J-tamed symplectic cones and J-compatible symplectic cones over a large class of almost complex manifolds…
Study para-complex structures on specific Lie groups, finding explicit forms and properties.
problem Characterizing para-Kähler structures on six-dimensional nilpotent Lie groups.
method Examined left-invariant para-complex structures on six-dimensional nilpotent Lie groups, obtained explicit expressions and investigated curvature properties.
result Para-complex structures are nilpotent and para-Kähler metrics are Ricci-flat.
Study on curvature properties of complex contact metric manifolds.
problem Understanding curvature properties in complex contact metric manifolds.
method Analyzing general results, deriving curvature tensor expressions, and establishing conditions for normality.
result Derived necessary and sufficient conditions for a complex contact metric manifold to be normal.
The paper studies how a specific flow preserves curvature properties on complex manifolds.
problem Preserving curvature properties over time on complex manifolds.
method Study of a Hermitian curvature flow (HCF) over compact complex Hermitian manifolds.
result The Griffiths positive (non-negative) Chern curvature is preserved along the flow.
Study automorphisms on procongruence curve and pants complexes.
problem Understanding automorphism groups of procongruence curve and pants complexes.
method Action on procongruence mapping class group and rigidity theorem for pants complex.
result Prove rigidity theorem for procongruence completion of pants complex.
Study complex hyperbolic lattices and their subgroups, proving new finiteness properties.
problem Characterize subgroups of complex hyperbolic lattices.
method Analyzing homomorphisms and using arithmetic lattice properties.
result Deep subgroups of complex hyperbolic lattices admit homomorphisms to Z with specific kernel types.