Groups with certain thickness have empty Floyd boundary.
problem Understanding Floyd boundaries of groups.
method Proving triviality of Floyd boundaries for thick groups.
result Trivial Floyd boundary for thick groups.
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48 results for “Floyd boundaries”
Extends Martin boundary to Floyd boundary for random walks.
problem Mapping Martin boundary to Floyd boundary for random walks.
method Continuous equivariant surjection using Green and Floyd metrics.
result Identity map extends to continuous surjection with preimages being singletons.
Study on Hausdorff dimension of boundaries of relatively hyperbolic groups.
problem Determining the Hausdorff dimension of boundaries of relatively hyperbolic groups.
method Examined Floyd and Bowditch boundaries, using uniformly conical points and Alhfors regular sets.
result Hausdorff dimension is a constant times the growth rate of the group.
The paper consists of two parts. In the first one we show that a relatively hyperbolic group splits as a star graph of groups whose central vertex group is finitely generated and the other vertex groups are maximal parabolic subgroups. As a corollary we obtain that every group which admits 3-discontinuous and 2-coc…
We introduce the notion of controlled Floyd separation between geodesic rays starting at the identity in a finitely generated group G. Two such geodesic rays are said to be Floyd separated with respect to quasigeodesics if the (Floyd) length of c-quasigeodesics (for fixed but arbitrary c) joining points on the geodesic…
Classifies nonorientable surfaces in a specific type of bundle.
problem Classifying surfaces in a specific type of bundle.
method Uses ideas from Floyd, Hatcher, and Thurston; puts surface in 'Morse position' with respect to the bundle projection.
result Classifies incompressible, boundary-incompressible, nonorientable surfaces.
Computes genus of specific knots using Floyd and Hatcher's tools.
problem Computing the genus of satellite tunnel number one knots and torti-rational knots.
method Uses Floyd and Hatcher's tools and an algorithm to compute genus and slopes of minimal genus Seifert surfaces.
result Computes genus and slopes for specific knots.
In this paper, we prove a limit set intersection theorem in relatively hyperbolic groups. Our approach is based on a study of dynamical quasiconvexity of relatively quasiconvex subgroups. Using dynamical quasiconvexity, many well-known results on limit sets of geometrically finite Kleinian groups are derived in general…
Adapts Floyd-Warshall algorithm for RL to improve multi-goal task learning.
problem Limited transfer of learned information in model-free RL for dynamic goal tasks.
method Adapts Floyd-Warshall algorithm for RL to learn goal-conditioned action-value functions.
result FWRL achieves higher reward strategies in multi-goal tasks with fewer samples.
The Martin boundary of certain groups is stable under specific conditions.
problem Stability of Martin boundaries in relatively hyperbolic groups.
method Extending Floyd-Ancona inequalities, defining spectral degenerescence, and proving stability criteria.
result The Martin boundary of admissible symmetric finitely supported probability measures on geometrically finite Kleinian groups of dimension at most 5 is always strongly stable.
The paper develops a theory of conformal density at infinity for groups with contracting elements.
problem Understanding conformal dynamics at infinity for groups with contracting elements.
method Introducing a class of convergence boundary and establishing the basic theory of conformal density on it.
result Unified theory of conformal density on various boundaries for different types of groups.
We show that Thurston's skinning maps of Teichmuller space have finite fibers. The proof centers around a study of two subvarieties of the SL_2(C) character variety of a surface, one associated to complex projective structures and the other associated to a 3-manifold. Using the Morgan-Shalen compactification of the cha…
Cannon, Floyd and Parry have studied the modulus of finite subdivision rules extensively. We investigate the properties of the modulus of subdivision rules with linear and exponential growth at every vertex, using barycentric subdivision and a subdivision rule for the Borromean rings as examples. We show that the subdi…
Culler and Shalen, and later Yoshida, give ways to construct incompressible surfaces in 3-manifolds from ideal points of the character and deformation varieties, respectively. We work in the case of hyperbolic punctured torus bundles, for which the incompressible surfaces were classified by Floyd and Hatcher. We conver…
We give uniform, explicit, and simple face-pairing descriptions of all the branched cyclic covers of the 3-sphere, branched over two-bridge knots. Our method is to use the bi-twisted face-pairing constructions of Cannon, Floyd, and Parry; these examples show that the bi-twist construction is often efficient and natural…
We obtain general formulae expressing Hirzebruch genera of a manifold with Z/p-action in terms of invariants of this action (the sets of weights of fixed points). As an illustration, we consider numerous particular cases of well-known genera, in particular, the elliptic genus. We also describe the connection with the s…
Generalizes theorem for topological -manifolds with linear Lie groups .
problem Understanding topological -manifolds with linear Lie groups .
method Using countable CW complexes and Palais-proper actions.
result Topological -manifolds have -homotopy type of countable -CW complexes.
In this paper, we determine the canonical polyhedral decomposition of every hyperbolic once-punctured torus bundle over the circle. In fact, we show that the only ideal polyhedral decomposition that is straight in the hyperbolic structure and that is invariant under a certain involution is the ideal triangulation defin…
Cannon, Floyd, and Parry have studied subdivisions of the 2-sphere extensively, especially those corresponding to 3-manifolds, in an attempt to prove Cannon's conjecture. There has been a recent interest in generalizing some of their tools, such as extremal length, to higher dimensions. We define finite subdivision rul…
Kawakubo and Uchida showed that, if a closed oriented -dimensional manifold admits a semi-free circle action such that the dimension of the fixed point set is less than , then the signature of vanishes. In this note, by using -signature theorem and the rigidity of the signature operator, we generaliz…
The paper solves a decades-old problem using complex bordism and Pontryagin duality.
problem A decades-old question raised by Iz Singer about complex bundles and their connections.
method Combining complex bordism, Pontryagin duality, and the APS Index Theorem to solve the problem.
result Stable complex bundles have complete numerical invariants computable by integrals of characteristic forms.
The paper explores growth rates and Perron numbers in Coxeter systems with low-dimensional Davis complexes.
problem Investigating growth rates and specific types of numbers in Coxeter systems with Davis complexes of low dimension.
method Examining Coxeter systems with Davis complexes of dimension at most 2, focusing on growth rates and specific types of numbers.
result The growth rate of Coxeter systems with Davis complexes of dimension at most 2 are either Salem or Pisot numbers, depending on the Euler characteristic.
Invariants for colored links found, with topological protection of certain knots.
problem Finding invariants for colored links and understanding their topological stability.
method Equivariant bordism groups of Conner and Floyd, topological surgeries.
result Topological protection of certain tricolored knots, with specific transformations.
Proves minimal growth rate for Coxeter groups in hyperbolic space.
problem Finding minimal growth rate Coxeter groups in hyperbolic space.
method Generalizes methods from cocompact case to non-cocompact groups.
result Proves minimal growth rate for Coxeter groups .
We simplify Thurston norm computation for 2-bridge link complements.
problem Understanding the complexity of Thurston norm unit balls in 3-manifolds.
method Utilized Floyd and Hatcher's surface description and integral class minimization.
result Thurston norm unit balls of 2-bridge link complements have at most 8 faces.
M/F-Theory as Mf-Theoryhep-th
New mathematical framework connects M-theory charges to stable homotopy groups.
problem Quantization of fluxes in M-theory and their mathematical representation.
method Establishing a correspondence between M-theory phenomena and stable homotopy theory concepts.
result Found a direct link between M-theory charges and stable homotopy groups.
Develops parametrised Poincaré duality for equivariant fixed points.
problem Understanding equivariant fixed points in non-presentable settings.
method Introduces parametrised Poincaré duality in parametrised higher category theory, proving basechange results.
result Generalises Cnossen's twisted ambidexterity to non-presentable settings and applies to isotropy separation methods.
Paper details Hilbert-curve for high-performance data mining.
problem Efficiently mapping multi-dimensional data to one dimension.
method Defines Hilbert-curve using finite automaton and context-free grammar.
result Cache-oblivious algorithms for matrix operations and clustering.
Reduces multiclass and regression compression schemes to binary ones.
problem Developing efficient learning algorithms for multiclass and regression problems.
method Reduces sample compression schemes for binary classes to multiclass and regression settings.
result Establishes new compression schemes for multiclass and regression problems.
Proves equivalence of two types of boundaries in metric spaces.
problem Proving equivalence of two types of boundaries in metric spaces.
method Analyzes and compares contracting and -Morse boundaries.
result Proves equivalence of 1-Morse boundary and contracting boundary as topological spaces.
Explicit formula derived for Slepian process boundary non-crossing probabilities.
problem Calculating boundary non-crossing probabilities for Slepian processes.
method Derived explicit formula and approximation formula for general continuous boundaries.
result Easy to implement formulas for boundary non-crossing probabilities.
Study boundary value problems for elliptic operators on manifolds.
problem Characterize and analyze boundary conditions for first-order elliptic differential operators.
method Develops a new framework for elliptic boundary conditions, proving equivalence and regularity of solutions.
result Elliptic boundary conditions yield a Fredholm operator on compact manifolds.
Proves unique extension of Bartnik boundary data for stationary vacuum spacetimes.
problem Unique extension of Bartnik boundary data for stationary vacuum spacetimes.
method Elliptic boundary value problem for stationary vacuum equations combined with Bartnik boundary conditions.
result Bartnik boundary data near standard flat data admits a unique stationary vacuum extension locally.
New symplectic boundary conditions for cohomology.
problem Defining cohomology for symplectic manifolds with boundary.
method Introducing elliptic boundary value problems and Hodge theories.
result Distinguishing Kähler structures of Kähler manifolds with boundary.
New corks found with Stein structures and hyperbolic boundaries.
problem Existence of boundary-sum irreducible finite order corks with Stein structures.
method Proved for any positive integer n, constructed corks with Stein structures and verified hyperbolic boundaries.
result Found boundary-sum irreducible -corks with Stein structures and verified hyperbolic boundaries.
Study defines a new boundary for CAT(0) groups, invariant under quasi-isometries.
problem Defining boundaries for CAT(0) groups when visual boundaries are not well-defined.
method Introducing a sublinear function κ to define κ-Morse boundaries, showing invariance under quasi-isometries.
result κ-Morse boundaries are invariant and metrizable for CAT(0) groups.
Proves well-posedness for Einstein equations with specific boundary conditions.
problem Well-posedness of vacuum Einstein equations with twisted Dirichlet boundary conditions.
method Proves local-in-time well-posedness for the IBVP of the Einstein equations with specified conformal class and scalar densities.
result Proves well-posedness for the Einstein equations with twisted Dirichlet boundary conditions.
Two surfaces with similar boundary distances are isometric.
problem Determining when two Riemannian surfaces are isometric based on boundary distances.
method Analyzing Riemannian metrics with specific properties and using boundary rigidity results.
result Two surfaces with the same marked boundary distance are isometric.
Abstracts a construction of boundary triplets for self-adjoint elliptic problems.
problem Computing the index of families of self-adjoint elliptic boundary problems.
method Abstract axiomatic version of boundary triplets and their applications.
result Analytic proof of index theorem and computation of index differences.
The paper studies Ricci flow on manifolds with boundary, proving existence, uniqueness, and boundary conditions preservation.
problem Ricci flow on manifolds with boundary.
method Proving short-time existence and uniqueness of the solution, and showing boundary conditions preservation.
result The flow preserves natural boundary conditions under certain curvature conditions.
Study shows boundary curves of free boundary minimal surfaces are circles.
problem Characterizing boundary curves of free boundary minimal surfaces.
method Holomorphic techniques applied to the unit ball in Euclidean 3-space.
result Intersection curves of free boundary minimal surfaces with the unit sphere are all circles.
Unique compact Fuchsian manifolds with convex boundary are determined by their boundary.
problem Identifying compact Fuchsian manifolds with convex boundaries.
method Proving uniqueness based on the induced path metric on the boundary.
result Compact Fuchsian manifolds with convex boundaries are uniquely determined by the induced path metric on the boundary.
Develops a new flow with free boundary in barrier surfaces.
problem Free-boundary problems in barrier surfaces.
method Develops Brakke flow with free boundary, proves compactness, Gaussian monotonicity, and existence.
result Proves existence of free-boundary Brakke flows.
We introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with rays that identify the "hyperbolic directions" in that space. This boundary is a quasi-isometry invariant and thus produces a well-defined boundary for any finitely generated group. In the case of a prope…
Generalizes Bestvina's -boundaries to coarse -boundaries.
problem Establishing properties of -boundaries for groups.
method Introducing a new concept of a 'coarse -boundary' and proving theorems about it.
result Admitting a coarse -boundary is a pure quasi-isometry invariant.
Study on quasi-Einstein manifolds with boundary estimates and inequalities.
problem Understanding the geometry of compact quasi-Einstein manifolds with boundary.
method Sharp boundary estimates and characterization theorems for quasi-Einstein manifolds.
result New geometric inequalities and boundary estimates for quasi-Einstein manifolds.
Concentration of -Lipschitz functions on manifolds with boundary with Dirichlet boundary conditionmath.MG
The paper studies concentration of measure on manifolds with boundary, focusing on -Lipschitz functions.
problem Concentration of measure phenomena of non-negative -Lipschitz functions on manifolds with Dirichlet boundary condition.
method Examined relation between boundary concentration phenomena and large spectral gap phenomena of Dirichlet eigenvalues of Laplacian. Introduced new invariant called the observable inscribed radius.
result Formulated comparison theorems for the observable inscribed radius under lower Ricci curvature and mean curvature bounds for the boundary.
Develops a novel classification boundary on Riemannian manifolds.
problem Classifying multivariate datasets on nonlinear Riemannian manifolds.
method Invents the principal boundary approach, defined as an optimal curve maximizing the margin between two classes.
result The principal boundary optimally separates classes and coincides locally with the SVM decision boundary.