Finite volume ends found in quaternionic Kähler manifolds.
problem Existence of quaternionic Kähler manifolds with finite volume ends.
method Proof in all dimensions .
result Existence of quaternionic Kähler manifolds with finite volume ends.
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.
169,341 papers · 148 categories
Trend · papers per month
48 results for “Finite Volume Manifolds”
Minimal surfaces found in finite volume manifolds.
problem Existence of minimal hypersurfaces in complete manifolds of finite volume.
method Independent result on volume sweeping by hypersurfaces; main tool is a volume constraint result.
result Proves existence of minimal hypersurfaces in complete non-compact manifolds of finite volume.
Entropy rigidity proven for 3D and higher convex projective manifolds.
problem Entropy rigidity for strictly convex projective manifolds.
method Uses techniques from Besson, Courtois, and Gallot's entropy rigidity theorem.
result Uniform lower bounds on volume for finite volume strictly convex projective manifolds in dimensions ≥ 3.
The study counts cusps on finite volume Riemannian manifolds using volume and decay estimates.
problem Counting cusps on finite volume Riemannian manifolds.
method Volume and decay estimates, nonlinear theory of p-Laplacian, volume comparison theorems.
result An upper bound on the number of cusps based on the volume of the manifold.
3-manifold volumes equal if finite quotients match.
problem Equal volume of 3-manifolds with same finite quotients.
method Lück's conjecture on torsion growth in homology.
result Equal volume of 3-manifolds with same finite quotients.
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…
Hyperbolic four-manifoldsmath.GT
Survey on finite-volume hyperbolic four-manifolds.
problem Finite-volume hyperbolic four-manifolds.
method No new methods are introduced.
result No new results are presented.
We show that complete uniform visibility manifolds of finite volume with sectional curvature have positive simplicial volumes. This implies that their minimal volumes are non-zero.
Entropy rigidity theorem for negatively curved finite volume manifolds.
problem Proving entropy rigidity for negatively curved manifolds of finite volume.
method Entropy rigidity result in finite volume, comparing with compact case.
result Isometry of manifolds with same length spectrum.
Totally umbilic surfaces in hyperbolic 3-manifolds are constructed and characterized.
problem Characterizing totally umbilic surfaces in hyperbolic 3-manifolds of finite volume.
method Construction and characterization of surfaces based on their properties and embedding conditions.
result Characterization of totally umbilic surfaces in hyperbolic 3-manifolds of finite volume.
Finite types of 4D manifolds with specific curvature, volume, and diameter.
problem Classifying 4D manifolds with given curvature, volume, and diameter constraints.
method Proving finiteness of diffeomorphism types for 4-manifolds with specified conditions.
result There are only finitely many diffeomorphism types of 4D manifolds with given curvature, volume, and diameter constraints.
The study shows simplicial volume finiteness for certain manifolds with amenable fundamental groups.
problem Determining the simplicial volume of manifolds with specific properties.
method Analyzing the fundamental group and using amenability properties.
result Simplicial volume is finite for certain manifolds with amenable fundamental groups.
Researchers create non-homogeneous finite-volume ends on quaternionic Kähler manifolds.
problem Constructing non-homogeneous quaternionic Kähler manifolds with finite volume ends.
method Using cohomogeneity one deformation of symmetric spaces, the researchers constructed manifolds with specific fundamental groups.
result The constructed manifolds are aspherical and have finite volume ends, not locally homogeneous.
It is known that the volume function for hyperbolic manifolds of dimension is finite-to-one. We show that the number of nonhomeomorphic hyperbolic 4-manifolds with the same volume can be made arbitrarily large. This is done by constructing a sequence of finite-sided finite-volume polyhedra with side-pairings t…
Totally geodesic submanifolds in convex cores are properly immersed and have finite volume.
problem Characterizing totally geodesic submanifolds in geometrically finite manifolds.
method Analysis of totally geodesic submanifolds in the convex core of geometrically finite rank-one locally symmetric manifolds.
result Every maximal totally geodesic submanifold of dimension at least two in the convex core is properly immersed and has finite volume, and only finitely many such submanifolds can occur.
Paper shows 3D hyperbolic manifolds are uniquely identified by their finite groups.
problem Identifying hyperbolic 3-manifolds using their finite quotient groups.
method Proves profinite isomorphism of fundamental groups uniquely determines the manifold's isomorphism type.
result Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups.
Researchers calculate the volume of Seifert representations for graph manifolds and their covers.
problem Computing the volume of Seifert representations for graph manifolds and their finite covers.
method Established an effective formula for computing the volume of Seifert representations of graph manifolds and obtained restrictions analogous to the Milnor–Wood inequality.
result The Seifert volume of any graph manifold is a rational multiple of π², and the supremum ratio of the Seifert volume over the covering degree can be positive or infinite.
Computational evidence supports that SnapPea census manifolds are distinguishable by their finite quotients.
problem Determining if non-isometric finite volume hyperbolic 3-manifolds are distinguishable by their finite quotients.
method Examined the SnapPea census of 72,942 manifolds and computed their finite quotients.
result No two manifolds in the SnapPea census have the same finite quotients.
The paper bends hyperbolic manifolds into convex structures.
problem Creating convex structures from hyperbolic manifolds.
method Bending totally geodesic hypersurfaces in finite volume hyperbolic manifolds.
result Examples of non-compact, finite volume, properly convex manifolds are found.
The study finds conditions for certain Riemannian manifolds to be graph manifolds.
problem Conditions for complete Riemannian manifolds with specific curvature properties to be graph manifolds.
method Analyzes necessary and sufficient conditions for manifolds with curvature nullity at least n-2.
result Nomizu's conjecture holds true for manifolds with finite volume and curvature nullity at least n-2.
We study noncompact, complete, finite volume, negatively curved manifolds . We construct with infinitely generated fundamental groups in all dimensions . We construct whose cusp cross sections are compact hyperbolic manifolds in all dimension . In contrast we show that if sectional curvatu…
Study shows simplicial volumes add for certain manifold gluings.
problem Understanding simplicial volumes in manifold gluings.
method Proves additivity of locally finite simplicial volume and Lipschitz simplicial volume for connected sums and specific boundary components.
result Additivity of simplicial volumes in dimension 3 and above for certain gluings.
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.
The rich theory of Coxeter groups is used to provide an algebraic construction of finite volume hyperbolic n-manifolds. Combinatorial properties of finite images of these groups can be used to compute the volumes of the resulting manifolds. Three examples, in 4,5 and 6-dimensions, are given, each of very small volume, …
In this article we study the spectrum of totally geodesic surfaces of a finite volume hyperbolic 3-manifold. We show that for arithmetic hyperbolic 3-manifolds that contain a totally geodesic surface, this spectrum determines the commensurability class. In addition, we show that any finite volume hyperbolic 3-manifold …
We compute the space of harmonic forms (outside the middle degrees) on negatively curved Kaehler manifolds of finite volume.
Study compares volumes of hyperbolic 3-manifolds using Ricci-DeTurck flow.
problem Volume comparison on finite-volume hyperbolic 3-manifolds.
method Exponential convergence of Ricci-DeTurck flow to the hyperbolic metric.
result The hyperbolic metric minimizes volume among metrics with bounded scalar curvature.
Open manifolds with nonnegative Ricci curvature and Euclidean volume growth have finitely generated fundamental groups.
problem Understanding fundamental groups of open manifolds with specific curvature properties.
method Analyzing universal covers with Euclidean volume growth and applying topological group theory.
result Fundamental groups are finitely generated and virtually abelian under given conditions.
The study establishes equivalence of conditions on metric manifolds with finite volume.
problem Characterizing metric spaces with a metric fundamental class.
method Analyzing three conditions on metric manifolds with finite volume.
result Conditions (1), (2), and (3) are equivalent for metric manifolds with finite Nagata dimension.
Let be the interior of a connected, oriented, compact manifold of dimension at least 2. If each path component of has amenable fundamental group, then we prove that the simplicial volume of is equal to the relative simplicial volume of and also to the geometric (Lipschitz) simplicial volume…
Degree theorems and Lipschitz simplicial volume for non-positively curved manifolds of finite volumemath.GT
We study a metric version of the simplicial volume on Riemannian manifolds, the Lipschitz simplicial volume, with applications to degree theorems in mind. We establish a proportionality principle and a product inequality from which we derive an extension of Gromov's volume comparison theorem to products of negatively c…
The paper contains a new proof that a complete, non-compact hyperbolic -manifold with finite volume contains an immersed, closed, quasi-Fuchsian surface.
Constructs manifolds with infinite Betti numbers and close to quadratic volume growth.
problem Understanding if manifolds with specific curvature bounds and volume growth must be of finite topological type.
method Constructs a family of dimensional open manifolds with positive Ricci curvature and sectional curvature bounds.
result Volume growth can be arbitrarily close to quadratic, and Betti numbers are infinite.
No spin structures found in a hyperbolic 4D space.
problem Finding hyperbolic 4-manifolds without spin structures.
method Constructed a non-compact, orientable, hyperbolic 4-manifold.
result Demonstrated existence of a hyperbolic 4D space without spin structures.
We compare the volume of a hyperbolic 3-manifold of finite volume and the complexity of its fundamental group.
The paper proves finite topological type theorems for open manifolds with non-negative Ricci curvature and almost maximal local rewinding volume.
problem Proving finite topological type theorems for open manifolds with non-negative Ricci curvature and almost maximal local rewinding volume.
method The approach removes constraints of sectional curvature or conjugate radius and extends to previous related studies.
result Theorems are proven for open manifolds with non-negative Ricci curvature and almost maximal local rewinding volume, without the need for triangle comparison of Toponogov type.
No CMC surfaces exist in certain hyperbolic 3-manifolds.
problem Existence of constant mean curvature (CMC) surfaces in hyperbolic 3-manifolds.
method Proof by contradiction using hyperbolic geometry and topology.
result Nonexistence of CMC surfaces with mean curvature ≥ 1.
The paper proves bounded domains are biholomorphic to the unit ball.
problem Covering manifolds with finite volume.
method Analyzes and boundary conditions for bounded domains.
result Bounded domains are biholomorphic to the unit ball under certain conditions.
Lower bounds for cover degrees of hyperbolic 3-manifolds.
problem Finding lower bounds for cover degrees of hyperbolic 3-manifolds.
method Using volume, diameter, and new invariants to establish lower bounds.
result Established lower bounds for cover degrees in terms of given parameters.
We prove new estimates for the volume of a Lorentzian manifold and show especially that cosmological spacetimes with crushing singularities have finite volume.
Uniform linear bounds on volume changes in 3D hyperbolic spaces.
problem Volume variation in hyperbolic 3-manifolds.
method Uniform linear bounds proof for drilling and filling operations.
result Uniform linear bounds on volume variation proved.
Study unimodular measures on Riemannian manifold spaces.
problem Understanding the geometry of large finite volume manifolds.
method Develop structure theory, use geodesic flow invariance, and characterize measures via foliations.
result Characterize unimodular measures and use them to compactify manifolds.
The paper studies Q-curvature and volume entropy on manifolds, proving polynomial growth polyharmonic function finiteness and rigidity.
problem Investigating Q-curvature and volume entropy on conformally flat manifolds.
method Introducing a new volume entropy, establishing identities, and proving rigidity results.
result Each polynomial growth polyharmonic function on such manifolds is of finite dimension, and the Cohn-Vossen inequality achieves equality under specific conditions.
We study the spectrum of the Dirac operator on hyperbolic manifolds of finite volume. Depending on the spin structure it is either discrete or the whole real line. For link complements in S^3 we give a simple criterion in terms of linking numbers for when essential spectrum can occur. We compute the accumulation rate o…
Infinite hyperbolic manifolds share same perimeter-to-volume ratio.
problem Finding hyperbolic manifolds with a fixed perimeter-to-volume ratio.
method Constructing infinitely many hyperbolic manifolds with nonempty boundaries.
result Existence of incommensurable hyperbolic manifolds with a fixed perimeter-to-volume ratio.
New 5D hyperbolic shapes that wrap around a circle found.
problem Finding new 5D hyperbolic structures.
method Examined finite-volume cusped hyperbolic 5-manifolds.
result Discovered the smallest known hyperbolic 5-manifold.
New noncompact manifolds with nonpositive curvature.
problem Creating new manifolds with specific curvature properties.
method Simple construction of manifolds with mixed ends.
result Found manifolds with fundamental groups not duality groups.
Study shows range of simplicial volumes for open manifolds.
problem Understanding simplicial volumes of open manifolds.
method Analyzes locally finite simplicial volumes in dimensions at least 4.
result Set of simplicial volumes is [0, ∞] for open manifolds.