In this paper we prove that the Kähler-Einstein metrics for a toroidal canonical degeneration family of Kähler manifolds with ample canonical bundles Gromov-Hausdorff converge to the complete Kähler-Einstein metric on the smooth part of the central fiber when the base locus of the degeneration family is empty. We also …
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48 results for “toroidal degeneration”
Study on how Kähler-Einstein metrics behave during degenerations of manifolds.
problem Behavior of Kähler-Einstein metrics during degenerations of manifolds.
method Analysis of collapsing behavior of negative Kähler-Einstein metrics along degenerations of canonical polarized manifolds.
result Kähler-Einstein metrics on fibers collapse to a lower dimensional complete Riemannian manifold in the pointed Gromov-Hausdorff sense.
Introduces new limit spaces for degenerating Calabi-Yau families.
problem Understanding degenerating Calabi-Yau families and their limit structures.
method Introduces galaxy spaces as dense subspace of infinite open Calabi-Yau varieties.
result Galaxy spaces are projective limits of toroidal compactifications.
We prove a theorem which bounds Heegaard genus from below under special kinds of toroidal amalgamations of -manifolds. As a consequence, we conclude for any pair of knots , where denotes the tunnel number of .
Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds I: Minimizationmath.DG
We construct embedded Willmore tori with small area constraint in Riemannian three-manifolds under some curvature condition used to prevent Möbius degeneration. The construction relies on a Lyapunov-Schmidt reduction; to this aim we establish new geometric expansions of exponentiated small symmetric Clifford tori and a…
This paper shows semi-equivelar toroidal maps are vertex-transitive covers.
problem Understanding the relationship between semi-equivelar and vertex-transitive toroidal maps.
method Proving semi-equivelar toroidal maps are quotients of vertex-transitive toroidal maps.
result Each semi-equivelar toroidal map has a finite vertex-transitive cover.
Proves a sharp inequality for toroidal surfaces in Horowitz-Myers geon.
problem Extending Minkowski inequality to non-static spacetimes.
method Proves a sharp inequality for toroidal hypersurfaces in Horowitz-Myers geon.
result Sharp inequality for toroidal surfaces in asymptotically hyperbolic manifold.
Characterizes toroidally alternating knots topologically.
problem Defining and characterizing toroidally alternating knots.
method Extending Howie's characterization to toroidally alternating knots and providing necessary and sufficient conditions.
result Necessary and sufficient conditions for a knot to be toroidally alternating.
Study bounds topological entropy of toroidal attractors.
problem Bounding entropy of toroidal attractors.
method Analyzing topological properties of toroidal sets to bound entropy.
result Entropy of toroidal attractors is bounded from below.
For a hyperbolic knot in the 3-sphere, at most finitely many Dehn surgeries yield non-hyperbolic 3-manifolds. As a typical case of such an exceptional surgery, a toroidal surgery is one that yields a closed 3-manifold containing an incompressible torus. The slope corresponding to a toroidal surgery, called a toroidal s…
The paper extends knot theory to annular and toroidal pseudo knots.
problem Defining and classifying pseudo knots in annular and toroidal settings.
method Introducing pseudo knots as equivalence classes under moves, lifting to torus, and exploring inclusion relations.
result New invariants for classifying pseudo knots and links in solid and thickened torus.
The paper characterizes toroidal sets as attractors for flows and homeomorphisms of R^3.
problem Characterizing toroidal sets as attractors for flows and homeomorphisms in R^3.
method Defined self-geometric index and genus to analyze toroidal sets and their attractor properties.
result Characterized toroidal sets that can be realized as attractors for flows but not for homeomorphisms.
Spectral Positive Mass Theorem for Asymptotically Hyperbolic 3-manifolds with Toroidal Infinitymath.DG
Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.
problem Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.
method Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.
result Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.
The study finds many Möbius bands and annuli on toroids.
problem Finding minimal surfaces on toroids.
method Equivariant variational methods.
result Linear growth of surface areas with symmetry order.
Extends results on automorphism groups of flat Minkowski planes to toroidal circle planes.
problem Understanding automorphism groups of toroidal circle planes.
method Extending Schenkel's results to toroidal circle planes.
result Automorphism groups of toroidal circle planes have dimensions at most 6 and can have dimensions at least 4 or kernels of dimension 3.
For a hyperbolic knot in the 3-sphere, the distance between toroidal surgeries is at most 5, except the figure eight knot. In this paper, we determine all hyperbolic knots that admit two toroidal surgeries with distance 5.
Characterizes knotted toroidal sets as attractors in 3D.
problem Characterizing knotted toroidal sets as attractors in .
method Global and local dynamical systems analysis, homeomorphisms and flows.
result Sufficient conditions for incompressible surfaces as attractors.
Classifies toroidal circle planes with 3D automorphism groups.
problem Classifying toroidal circle planes with specific automorphism groups.
method Using almost simple Lie groups and their isomorphism to PSL(2, R), a framework for classification is described.
result Three-dimensional connected automorphism groups are isomorphic to PSL(2, R).
Study shows infinitely many ways to compactify surfaces as ball quotients.
problem Realizing smooth projective surfaces as ball quotient compactifications.
method Constructing families of distinct ball quotients with biholomorphic smooth toroidal compactifications.
result Arbitrarily large families of distinct ball quotients with biholomorphic smooth toroidal compactifications.
If a simple 3-manifold M admits a reducible and a toroidal Dehn filling, the distance between the filling slopes is known to be bounded by three. In this paper, we classify all manifolds which admit a reducible Dehn filling and a toroidal Dehn filling with distance 3.
Optimal Euclidean structure minimizes energy in weighted toroidal graphs.
problem Finding the optimal Euclidean structure for weighted toroidal graphs.
method Minimizing Dirichlet energy over all possible Euclidean structures and realizations within a fixed homotopy class.
result The optimal Euclidean structure induces a weighted Delaunay decomposition.
The study classifies and constructs toroidal compactifications of smooth complex hyperbolic surfaces.
problem Classifying and constructing toroidal compactifications of smooth complex hyperbolic surfaces.
method Explicit construction and classification of minimum volume smooth complex hyperbolic surfaces that admit smooth toroidal compactifications.
result There are five such surfaces, all arithmetic and associated with commensurable arithmetic lattices.
The article proves and are toroidal penny graphs.
problem Optimal sphere packing on torus.
method Analyzing connections between planar graphs, penny graphs, and toroidal penny graphs.
result and are toroidal penny graphs.
The paper extends knot polynomials to annular and toroidal pseudo links.
problem Analyzing pseudo links with undefined crossings.
method Introducing Kauffman bracket and Jones-type polynomials for annular and toroidal pseudo links.
result New tools for studying annular and toroidal pseudo links.
Toroidal 3-manifolds have special group structures that can be shown through specific covers.
problem Characterizing the fundamental groups of toroidal 3-manifolds.
method Proving toroidal 3-manifolds have circularly-orderable fundamental groups by showing they admit finite cyclic covers with left-orderable fundamental groups.
result Toroidal 3-manifolds have circularly-orderable fundamental groups, which can be shown through specific covers.
T-PSDA improves speaker recognition accuracy on toroidal submanifolds.
problem Improving speaker recognition accuracy on hypersphere embeddings.
method Extends PSDA to model within and between-speaker variabilities in toroidal submanifolds of the hypersphere.
result T-PSDA achieves accuracy on par with cosine scoring on VoxCeleb and large accuracy gains on NIST SRE'21.
Semi-toric and toroidal compactifications as log minimal models, and applications to weak K-modulimath.AG
Characterizes toroidal and semi-toric compactifications as log minimal models and applies to weak K-moduli.
problem Characterizing and applying toroidal and semi-toric compactifications to weak K-moduli.
method Characterizes toroidal and semi-toric compactifications as log minimal models and applies to weak K-moduli.
result Different proof of a theorem of Alexeev-Engel on weak K-moduli compactifications.
The paper extends knotoid theory to annular and toroidal settings.
problem Extending knotoid theory to new geometric settings.
method Introducing new knotoid types, extending bracket polynomials.
result Universal bracket polynomials for annular and toroidal knotoids.
Solves Skopenkov's problem on graph embedding criteria.
problem Criteria for toroidal embedding of one-vertex ribbon graphs.
method Analyzes one-vertex ribbon graphs with additional disc structure.
result Provides solutions to Skopenkov's problem.
New types of knot mosaics help count and analyze knots efficiently.
problem Counting and analyzing knots efficiently.
method Introducing period and toroidal knot mosaics and developing algorithms for their enumeration.
result Exact enumeration of period knot mosaics and asymptotics of toroidal knot mosaics.
We give a complete classification of toroidal Seifert fibered surgeries on alternating knots. Precisely, we show that if an alternating knot admits a toroidal Seifert fibered surgery, then the knot is either the trefoil knot and the surgery slope is zero, or the connected sum of a (2,p)-torus knot and a (2,q)-torus kno…
Mixing endomorphisms found on toroidal groups and their products.
problem Finding topologically mixing endomorphisms on toroidal groups and their products.
method Analyzing continuous endomorphisms on toroidal groups and their countable products.
result Proves existence of infinitely many topologically mixing endomorphisms on countable infinite toroidal groups.
We show that if a Montesinos knot admits a Dehn surgery yielding a toroidal Seifert fibered 3-manifold, then the knot is the trefoil knot and the surgery slope is 0.
We study the classification of smooth toroidal compactifications of nonuniform ball quotients in the sense of Kodaira and Enriques. Moreover, several results concerning the Riemannian and complex algebraic geometry of these spaces are given. In particular we show that there are compact complex surfaces which admit Riem…
Proves Dolbeault cohomology conjecture for complex nilmanifolds foliated by tori.
problem Computing Dolbeault cohomology of complex nilmanifolds.
method Generalizes previous methods by assuming foliation in toroidal groups.
result Conjecture holds in real dimension up to six.
3-manifold groups are rigid under certain conditions.
problem Understanding the rigidity of 3-manifold groups.
method Analyzing compact, orientable, irreducible 3-manifolds with specific boundary conditions.
result Fundamental groups of these 3-manifolds are Grothendieck rigid.
Exceptional Dehn surgeries have been classified for 2-bridge knots and Montesinos knots of length at least 4. In this paper we classify all toroidal Dehn surgeries on Montesinos knots of length 3.
New positive mass theorems for ALH manifolds with toroidal ends.
problem Proving positive mass theorems for asymptotically locally hyperbolic manifolds.
method Utilizes properties of marginally outer trapped surfaces and a new technique involving μ-bubbles.
result Obtained new positive mass theorems for asymptotically locally hyperbolic manifolds without boundary.
Curvature properties and Shafarevich conjecture for toroidal compactifications of ball quotientsmath.CV
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.
Detect slopes in toroidal 3-manifolds to prove properties of fundamental groups.
problem Prove properties of fundamental groups of toroidal 3-manifolds.
method Slope detection using left-orders, foliations, and Heegaard Floer homology.
result Toroidal integer homology spheres have left-orderable fundamental groups.
Let M be a simple 3-manifold with a toral boundary component partial_0 M. If Dehn filling M along partial_0 M one way produces a toroidal manifold and Dehn filling M along partial_0 M another way produces a boundary-reducible manifold, then we show that the absolute value of the intersection number on partial_0 M of th…
We classify the smallest finite volume complex hyperbolic surfaces with cusps which admit smooth toroidal compactifications and which are not birational to a bi-elliptic surface. Remarkably, there is only one such surface which appears to be the compactification of a Picard modular surface.
Defines monopole Floer homology for 3-manifolds with toroidal boundaries.
problem Calculating invariants of 3-manifolds with toroidal boundaries.
method Develops monopole Floer homology using 3+1 topological quantum field theory.
result Euler characteristic recovers Milnor-Turaev torsion invariant.
The main goal of the present paper is two-fold. First we extend the theory of toroidal embeddings introduced by Kempf, Knudsen, Mumford and Saint-Donat to the class of toroidal varieties with stratifications (which is the main body of the paper). Second we give a proof of the following weak factorization theorem as an …
Finite slope cyclic surgeries along toroidal Brunnian links and generalized Properties P and Rmath.GT
Finite slope surgeries on certain links yield specific 3-manifolds.
problem Determining when finite slope surgeries on Milnor links yield lens spaces.
method Alexander polynomials and Reidemeister torsions.
result Finite slope surgeries on Milnor links do not yield lens spaces for λ ≥ 4.
Method to create rational Seifert surfaces for knots in Lens space.
problem Creating rational Seifert surfaces for knots in Lens space.
method Assuming a regular projection, construct rational Seifert surface on twist toroidal diagram.
result A method to construct rational Seifert surfaces for knots in Lens space.
The paper proves energy theorems for specific initial data sets in 3D spacetime.
problem Establishing energy theorems for specific initial data sets in 3D spacetime.
method Analysis of level sets of spacetime harmonic functions.
result Rigidity results showing vanishing total energy imply isometric manifolds.
We determine all hyperbolic 3-manifolds admitting two toroidal Dehn fillings at distance 4 or 5. We show that if is a hyperbolic 3-manifold with a torus boundary component , and are two slopes on with or 5 such that and both contain an essential torus, then is eit…