New Klein-Maskit theorems for Anosov subgroups.
problem Creating new Kleinian groups from old ones.
method Analogous combination theorems for Anosov subgroups.
result Construct new Kleinian groups using old ones for Anosov subgroups.
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48 results for “combination theorem”
We prove a combination theorem for trees of (strongly) relatively hyperbolic spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives a geometric extension of Bestvina and Feighn's Combination Theorem for hyperbolic groups and answers a question of Swarup. We also prove a converse to the main Com…
Survey of combination theorems in geometry and dynamics.
problem Combination theorems in hyperbolic geometry, group theory, and dynamics.
method Survey and focus on Thurston's contributions.
result Thurston's influence on combination theorems.
Study continuous paths in discrete subgroups of hyperbolic space, proving combination and decomposition theorems.
problem Understanding continuous paths in discrete subgroups of hyperbolic space.
method Combination theorem and chromatography technique.
result Construction of an exotic path of discrete subgroups with no isomorphic subgroups.
In this paper, we generalise the first Klein-Maskit combination theorem to discrete groups of Möbius transformations in higher dimensions. As a simple application of the main theorem, some examples will be constructed.
Combination theorem for PGF groups helps in constructing new examples and understanding their geometry.
problem Understanding the geometry of PGF groups and their combinations.
method Utilizing subsurface projection to control the geometry of fundamental groups of graphs of PGF groups.
result Combination theorem for PGF groups and other generalizations.
Combination theorems for convex projective geometry subgroups.
problem Understanding discrete subgroups in convex projective geometry.
method General combination theorems for discrete subgroups preserving properly convex open subsets.
result Free products of convex cocompact subgroups are convex cocompact.
The study proves a tube theorem for complex hyperbolic manifolds.
problem Understanding the geometry of complex hyperbolic manifolds.
method Tubular neighborhood theorem and geometric combination theorem.
result Explicit estimates and bounds for tube widths in complex hyperbolic manifolds.
In this paper we prove a combination theorem for Veech subgroups of the mapping class group analogous to the first Klein-Maskit combination theorem for Kleinian groups in which two Fuchsian subgroups are amalgamated along a parabolic subgroup. As a corollary, we construct subgroups of the mapping class group (for all g…
Generalizes Klein-Maskit theorem to free products of Anosov subgroups.
problem Proving a generalization of Klein-Maskit theorem for free products of Anosov subgroups.
method Analyzing Anosov subgroups in free products of semisimple Lie groups.
result The group generated by free products of Anosov subgroups is again Anosov and isomorphic to the free product.
The study combines graph-minors and metric spaces, answering some questions and conjectures.
problem Whether geodesic metric spaces without a fat minor are quasi-isometric to graphs without minor.
method Combining graph-minors and coarse geometry, answering affirmatively for small .
result Affirmative answer for small in the problem statement.
We give a short topological proof for Rubermans Theorem about mutation and volume, using the Maskit combination theorem and the homology of the linear group.
The paper explores new phenomena in boundaries of relatively hyperbolic groups.
problem Exploring new phenomena in boundaries of relatively hyperbolic groups.
method Combination theorem to create examples of relatively hyperbolic groups with parabolic cut pairs.
result All relatively hyperbolic groups with inseparable parabolic cut pairs arise via the combination theorem.
Combination theorem for geodesic coarsely convex group pairs.
problem Understanding properties of groups relative to subgroups.
method Definitions of weakly semihyperbolic, semihyperbolic, and geodesic coarsely convex group pairs; combination theorem.
result Combination theorem for geodesic coarsely convex group pairs.
We extend the validity of the Penrose singularity theorem to spacetime metrics of regularity . The proof is based on regularisation techniques, combined with recent results in low regularity causality theory.
The paper describes a structural decomposition of a specific type of Schottky groups.
problem Understanding the structure of extended -Schottky groups.
method Using Klein-Maskit's combination theorems.
result A structural decomposition theorem for extended -Schottky groups.
We first proved a compactness theorem of the Kähler metrics, which confirms a prediction of Chen. Then we prove several eigenvalue estimates along the Calabi flow. Combining the compactness theorem and these eigenvalue estimates, we generalize the method developed by Chen-Li-Wang to prove the small energy theorems of t…
In this article, we prove a combination theorem for a complex of relatively hyperbolic groups. It is a generalization of Martin's \cite{martin} work for combination of hyperbolic groups over a finite -simplicial complex, where .
The purpose of this survey is to present analytic versions of the injectivity theorem and their applications. The proof of our injectivity theorems is based on a combination of the L^2-method for the dbar-equation and the theory of harmonic integrals. As applications, we obtain Nadel type vanishing theorems and extensi…
In this paper, we state two combination theorems for relatively quasiconvex subgroups in a relatively hyperbolic group. Applications are given to the separability of double cosets of certain relatively quasiconvex subgroups and the existence of closed surface subgroups in relatively hyperbolic groups.
Hadwiger's Theorem states that Euclidean-invariant convex-continuous valuations of definable sets are linear combinations of intrinsic volumes. We lift this result from sets to data distributions over sets, specifically, to definable real-valued functions on n-dimensional Euclidean space. This generalizes intrinsic vol…
The paper proves a new inequality for 3-manifolds with noncompact boundaries.
problem Proving positivity of a convex combination of ADM masses on 3-manifolds with noncompact boundaries.
method Obtained an integral inequality for asymptotically linear harmonic functions.
result Positivity of a convex combination of ADM masses under a positivity condition on scalar curvatures and boundary mean curvatures.
Paper resolves Huisken's conjecture without strict genus drop theorem.
problem Huisken's genericity conjecture in mean curvature flow in R^3.
method Short density-drop theorem + Bamler-Kleiner multiplicity-one theorem for tangent flows.
result Fully resolves Huisken's conjecture without strict genus drop theorem.
We prove analogues for Cartan geometries of Gromov's major theorems on automorphisms of rigid geometric structures. The starting point is a Frobenius theorem, which says that infinitesimal automorphisms of sufficiently high order integrate to local automorphisms. Consequences include a stratification theorem describing…
In this paper, we study the critical case of the Allard regularity theorem. Combining with Reifenberg's topological disk theorem, we get a critical Allard-Reifenberg type regularity theorem. As a main result, we get the topological finiteness for a class of properly immersed surfaces in with finite Willm…
New Witten rigidity theorems for elliptic genus in various dimensions.
problem Proving rigidity theorems for elliptic genus in different dimensions.
method Combining Liu's and Han-Yu's methods to prove Witten rigidity theorems for elliptic genus in even and odd dimensions.
result Several new Witten rigidity theorems for elliptic genus in even and odd dimensions have been established.
We show in this short note that if a rational linear combination of Pontrjagin numbers vanishes on all simply-connected -dimensional closed connected and oriented spin manifolds admitting a Riemannian metric whose Ricci curvature is nonnegative and nonzero at any point, then this linear combination must be a multip…
Proves mass theorem up to dimension 19 using symmetrization and singularity techniques.
problem Proving the Riemannian positive mass theorem up to dimension 19.
method Combining toric symmetrization and singularity blow-up techniques.
result Proves the Riemannian positive mass theorem up to dimension 19.
New integral theorems improve density function estimations.
problem Improving density function estimations.
method Integrals based on cyclic functions and Riemann sums, Fourier integral theorem, Monte Carlo methods, variational approach, Cauchy residue theorem.
result Optimal cyclic functions minimize square integrals, improving density estimations.
In this paper, we first establish an -equivariant index theorem for Spin Dirac operators on manifolds, then combining with the methods developed by Taubes \cite{MR998662} and Liu-Ma-Zhang \cite{MR1870666,MR2016198}, we extend Witten's rigidity theorem to the case of Spin manif…
The paper proves lower bounds for Gaussian-weighted curvature integrals of self-shrinkers.
problem Proving lower bounds for Gaussian-weighted \(L^2\)-curvature integrals of self-shrinkers.
method Combining normal coordinate functions with weighted Poincaré inequalities and first-eigenvalue estimates.
result Explicit lower bounds in terms of entropy for closed self-shrinkers, leading to curvature gaps.
We show the mapping class group, CAT(0) groups, the fundamental groups of closed 3-manifolds, and certain relatively hyperbolic groups have a local-to-global property for Morse quasi-geodesics. This allows us to generalize combination theorems of Gitik for quasiconvex subgroups of hyperbolic groups to the stable subgro…
Discrete curvaturemath.DG
Survey on discrete curvature concepts for polygons and polyhedral surfaces.
problem Defining curvature for discrete structures like polygons and polyhedral surfaces.
method Explains curvature notions for polygons, polyhedral surfaces, and abstract polyhedral manifolds.
result Discrete curvature theorems parallel classical theorems in differential geometry.
For proper surjective holomorphic maps from K"ahler manifolds to analytic spaces, we give a decomposition theorem for the cohomology groups of the canonical bundle twisted by Nakano semi-positive vector bundles by means of the higher direct image sheaves, by using the theory of harmonic integrals developed by Takegoshi…
New proof classifies ancient flows in 3D space.
problem Classifying ancient noncollapsed flows in .
method Combining neck theorem and Harnack inequality rigidity.
result Directly establishes self-similarity of flows.
Geometric theory of integration developed in SDG.
problem Combining infinitesimal contributions to finite quantities.
method Analysis of differential forms and new operators in SDG.
result Discovery of new types of differential forms and operators.
A Fenchel Theorem for the Gauss maps and uniqueness of minimizers of nonlocal curvature energiesmath.CA
The paper proves a Fenchel theorem for Gauss maps and shows circles and disks minimize certain energies.
problem Finding minimizers of nonlocal curvature energies.
method Combining Fenchel-type theorems with geometric analysis techniques.
result Circles and disks minimize specific energy functionals.
Survey simplifies embedding theorems for manifolds.
problem Embedding manifolds into Euclidean space.
method Combining complement and neighborhood ideas to reduce embeddability to algebraic problems.
result Clarified exposition of Browder-Levine theorem on realization of normal systems.
Here we explore a variety of properties of intrinsic flat convergence. We introduce the sliced filling volume and interval sliced filling volume and explore the relationship between these notions, the tetrahedral property and the disappearance of points under intrinsic flat convergence. We prove two new Gromov-Hausdorf…
Vanishing result for cohomology leads to extension theorem for pluriharmonic functions.
problem Extension of pluriharmonic functions on complex manifolds.
method Vanishing result for Bott-Chern cohomology combined with Ehrenpreis technique.
result Hartogs extension theorem for pluriharmonic functions on cohomologically -complete manifolds.
We prove that a group obtained as a quotient of the free product of finitely many cubulable groups by a finite set of relators satisfying the classical --small cancellation condition is cubulable. This yields a new large class of relatively hyperbolic groups that can be cubulated, and constitutes the first ins…
The paper finds optimal ways to combine ETFs to minimize costs for investors.
problem Finding the best combination of ETFs to match a target gearing ratio at the lowest expense.
method Linear programming and convex geometry to prove the two-fund theorem for ETFs.
result The cheapest way to achieve a target gearing ratio is by combining the two nearest undominated ETF products.
Low regularity spacetimes split into simpler structures.
problem Proving splitting theorem for metrics and weights.
method Combining elliptic techniques and line-adapted curves.
result Extends Lorentzian splitting theorem to settings.
We prove a generalization of Livsic's Theorem on the vanishing of the cohomology of certain types of dynamical systems. As a consequence, we strengthen a result due to Zimmer concerning algebraic hulls of Anosov actions of semisimple Lie groups. Combining this with Topological Superrigidity, we find a Holder geometric …
We define metric bundles/metric graph bundles which provide a purely topological/coarse-geometric generalization of the notion of trees of metric spaces a la Bestvina-Feighn in the special case that the inclusions of the edge spaces into the vertex spaces are uniform coarsely surjective quasi-isometries. We prove the e…
New rigidity theorem on static manifolds with boundary.
problem Static metrics on manifolds with boundary.
method Obata-type rigidity theorem, sufficient geometric conditions.
result Scalar curvature map can be locally surjective at static metrics on manifolds with boundary.
We establish several Witten type rigidity and vanishing theorems for twisted Toeplitz operators on odd dimensional manifolds. We obtain our results by combining the modular method, modular transgression and some careful analysis of odd Chern classes for cocycles in odd -theory. Moreover we discover that in odd dimen…
In this paper we prove a stability theorem for block diffeomorphisms of 2d-dimensional manifolds that are connected sums of S^d x S^d. Combining this with a recent theorem of S. Galatius and O. Randal-Williams and Morlet's lemma of disjunction, we determine the homology of the classifying space of their diffeomorphism …