Finite-type surfaces have a topological Hopf property.
problem Characterizing surfaces with a topological Hopf property.
method Using topological analogs of the Hopf property.
result Infinite-type surfaces do not have the Hopf property.
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48 results for “finite type surface”
Proofs for Gauss map properties on surfaces with finite geometric type.
problem Properties of Gauss maps on surfaces with finite geometric type.
method Topological proof and generalization of the little Picard theorem.
result Gauss map can not omit three or more points for minimal and no flat surfaces.
Submanifolds of coordinate finite-type were introduced in HV1. A submanifold of a Euclidean space is called a coordinate finite-type submanifold if its coordinate functions are eigenfunctions of Δ. In the present study we consider coordinate finite-type surfaces in E^4. We give necessary and sufficient conditions for g…
In this paper, we study ruled surfaces and quadrics in the 3-dimensional Euclidean space which are of finite -type, that is, they are of finite type, in the sense of B.-Y. Chen, with respect to the third fundamental form. We show that helicoids and spheres are the only ruled and quadric surfaces of finite -ty…
Finite rigid sets found in complex of curves for surfaces.
problem Finding finite rigid sets in curve complexes of surfaces.
method Exhaustion by finite rigid sets proved for surfaces of finite type and genus ≥3.
result Finite rigid sets exist in the non-separating curve complex of surfaces.
Study of infinite-type surfaces' automorphisms and graph structures.
problem Understanding automorphisms of infinite-type surfaces.
method Isomorphic mappings between extended mapping class groups and graph automorphism groups.
result Extended mapping class groups are isomorphic to graph automorphism groups.
Characterizes monodromies of projective structures on finite-type surfaces.
problem Understanding monodromies of projective structures on finite-type surfaces.
method Geometrical/topological study of local conical projective structures.
result Any representation can be represented as the holonomy of a branched projective structure.
New proof shows special surfaces have finite type.
problem Characterizing surfaces with finite topological type.
method Shorter proof of Huber's theorem.
result Special surfaces have finite topological type.
Finite-type k-surfaces in hyperbolic space have finite genus and cusp-like ends.
problem Characterizing the geometry of finite-type k-surfaces in hyperbolic space.
method Analyzing the asymptotic behavior and geometric properties of finite-type k-surfaces.
result Finite-type k-surfaces have well-defined Steiner geodesics and points, leading to new geometric identities.
An approximation theorem for minimal surfaces by complete minimal surfaces of finite total curvature in is obtained. This Mergelyan type result can be extended to the family of complete minimal surfaces of weak finite total curvature, that is to say, having finite total curvature on proper regions of fin…
In this paper, we study the Lorentzian minimal surfaces in the Minkowski space-time with finite type Gauss map. First, we obtain the classification of this type of surfaces with pointwise 1-type Gauss map. Then, we proved that there are no Lorentzian minimal surface in the Minkowski space-time with null 2-type Gauss ma…
A maximal surface $\sb$ with isolated singularities in a complete flat Lorentzian 3-manifold is said to be entire if it lifts to a (periodic) entire multigraph $\tilde{\sb}$ in In addition, $\sb$ is called of finite type if it has finite topology, finitely many singular points and $\tilde{\sb}$ is finitely …
Proof of surface homeomorphism classification theorem.
problem Classify homeomorphisms of surfaces of finite type.
method Neilsen-Thurston classification theorem proof.
result Proof of Nielsen-Thurston theorem for surfaces of finite type.
This thesis introduces big mapping class groups and their structure.
problem Understanding mapping class groups of infinite-type surfaces.
method Systematic introduction and analysis of structure and topological generation.
result Key differences from finite-type mapping class groups.
Extends Nielsen realization to infinite-type surfaces, classifying torsion elements and topological groups.
problem Realizing finite subgroups of mapping class groups on infinite-type surfaces.
method Extending Kerckhoff's result to infinite-type surfaces, using hyperbolic metrics and topological group properties.
result Compact subgroups of mapping class groups are finite, and locally compact subgroups are discrete.
This paper studies finite type invariants for welded string links and ribbon tubes, showing characterizations and algebraic structures.
problem Finite type invariants for ribbon knotted surfaces and their relation to welded string links.
method Developed a theory of finite type invariants for welded string links up to -equivalence, studied algebraic structures, and showed characterizations.
result Characterizes the information contained by finite type invariants in low degrees for welded string links.
Study on compact and finite-type support in mapping class group homology.
problem Understanding non-trivial classes supported on compact or finite-type subsurfaces.
method Use of shiftable subsurfaces and homological stability for finite-type surfaces.
result Almost-complete answer for surfaces with positive genus, partial answer for zero genus.
Book explores infinite translation surfaces, challenging traditional geometry.
problem Understanding infinite-type translation surfaces.
method Detailed classification, construction, and analysis of symmetries.
result Complex dynamics in infinite-type translation flows.
This study defines finite-type invariants for curves on surfaces and reveals the construction of these finite-type invariants for stable homeomorphism classes of curves on compact oriented surfaces without boundaries. These invariants are a higher-order generalisation of a part of Arnold's invariants that are first-ord…
Study properties of surfaces with nonvanishing third fundamental form.
problem Investigate surfaces with finite III-type properties.
method Analyze Laplace operators and third fundamental form of surfaces in E3.
result Present surfaces of revolution with constant R and nonvanishing Gauss curvature.
Extending our previous work on eigenvalues of closed surfaces and work of Otal and Rosas, we show that a complete Riemannian surface S of finite type and negative Euler characteristic has at most negative of the Euler characteristics many small eigenvalues.
Non-collapsed finite time singularities of the Ricci flow on compact Kähler surfaces are of Type Imath.DG
Ricci flow singularities on compact Kähler surfaces are of Type I.
problem Understanding finite time singularities of Ricci flow on compact Kähler surfaces.
method Analyzing the Type I property of singularities.
result Non-collapsed finite time singularities are of Type I.
Countable modular groups found on surfaces with infinite type.
problem Finding modular groups of infinite type surfaces.
method Proving countable modular groups for orientable infinite type surfaces.
result Every orientable infinite type surface has a countable modular group.
Study on Gauss map surfaces in 3D space, focusing on anchor rings.
problem Classifying finite type Gauss map surfaces in Euclidean 3-space.
method Investigating a subclass of tubes, anchor rings, and analyzing their Gauss map properties.
result Anchor rings are of infinite type Gauss map.
Study of infinite type surfaces' mapping class groups via hyperbolic structures.
problem Understanding mapping class groups of infinite type surfaces.
method Definition of a topology on a moduli space of marked hyperbolic structures.
result Continuous action of mapping class groups on the marked moduli space.
New coefficient detects irrational rotation behavior on infinite-type surfaces.
problem Detecting irrational rotation behavior on surfaces of infinite type.
method Introducing a new quasimorphism, the Dehn twist coefficient, and proving its properties.
result The Dehn twist coefficient can have image all of R for some infinite-type surfaces.
We propose a general framework for constructing and describing infinite type flat surfaces of finite area. Using this method, we characterize the range of dynamical behaviors possible for the vertical translation flows on such flat surfaces. We prove a sufficient condition for ergodicity of this flow and apply the cond…
For a hyperbolic surface S of finite type we consider the set A(S) of angles between closed geodesics on S. Our main result is that there are only finitely many rational multiples of πin A(S).
Study decomposes geometric surfaces, finding special curves.
problem Existence of certain affine diffeomorphisms on translation surfaces.
method Explicit cylinder decomposition on geometric surfaces.
result Special curves are obstructions to certain diffeomorphisms.
Survey on quadratic differentials in Teichmüller theory.
problem Understanding quadratic differentials in Teichmüller theory.
method Expository survey of quadratic differentials' roles.
result Summarizes results for non-compact surfaces.
Study of flip graphs and their automorphism groups for infinite-type surfaces.
problem Understanding automorphism groups of flip graphs for infinite-type surfaces.
method Examined the relationship between mapping class groups and flip graphs for infinite-type surfaces.
result Extended mapping class groups are isomorphic to proper subgroups of automorphism groups of flip graphs.
The aim of this survey is to give an overview on the geometry of Einstein maximal globally hyperbolic 2+1 spacetimes of arbitrary curvature, conatining a complete Cauchy surface of finite type. In particular a specialization to the finite type case of the canonicla Wick rotation-rescaling theory, previously developed b…
Tileable Surfacesmath.DG
Constructs surfaces that can be tiled by a finite set of rigid motion congruence classes of tiles.
problem Creating surfaces that can be tiled by a finite set of rigid motion congruence classes of tiles.
method Constructs examples with various topologies and describes all monotilings by finite edge prototiles.
result Describes all monotilings by finite edge prototiles with three or less edges.
We investigate some relations concerning the first and the second Beltrami operators corresponding to the fundamental forms I, II, III of a surface in the three-dimensional Euclidean space and we study surfaces which are of finite type in the sense of B.-Y. Chen with respect to the fundamental forms II and III.
Covers of surfacesmath.GT
Study covers of surfaces, showing types and properties.
problem Characterize homeomorphism types of surface covers.
method Analyzing homeomorphism types of covers of surfaces, identifying universal covers and homology covers.
result Identify four possible homeomorphism types for certain covers of surfaces.
We show that any isomorphism between mapping class groups of orientable infinite-type surfaces is induced by a homeomorphism between the surfaces. Our argument additionally applies to automorphisms between finite-index subgroups of these `big' mapping class groups and shows that each finite-index subgroup has finite ou…
Uniform hyperbolicity proved for nonorientable surface curve graphs.
problem Proving uniform hyperbolicity for nonorientable surface curve graphs.
method Using bicorn curves and arguments from orientable surfaces.
result Graph of nonseparating curves is uniformly hyperbolic.
The paper studies circle patterns on surfaces with specific angles and curvature maps.
problem Investigating circle patterns with obtuse angles on surfaces of finite type.
method Characterizing curvature maps and establishing combinatorial Ricci flow conditions.
result Generalizations of circle pattern theorem and a computational method to find patterns.
The paper defines infinite Schottky groups and their applications to infinite type surfaces.
problem Understanding group actions on infinite type surfaces.
method Definition and analysis of infinite Schottky groups and their properties.
result Every infinite type Riemann surface can be obtained as a quotient of a region of discontinuity of an infinite Schottky group.
Paper constructs hyperbolic metrics using circle packings and curvature parameters.
problem Creating polyhedral metrics for surfaces of various topologies.
method Using circle packings and curvature parameters, the paper constructs hyperbolic polyhedral metrics.
result Unified approach to producing polyhedral metrics for surfaces of broader topological types.
Big mapping class groups of infinite type surfaces have infinite asymptotic dimension.
problem Understanding asymptotic dimension of big mapping class groups of infinite type surfaces.
method Analyzing big mapping class groups with coarsely bounded generating sets and essential shifts.
result Big mapping class groups of infinite type surfaces have infinite asymptotic dimension.
We study symplectic deformation types of minimal symplectic fillings of links of quotient surface singularities. In particular, there are only finitely many symplectic deformation types for each quotient surface singularity.
We obtain a Chern-Osserman type equality of a complete properly immersed surface in Euclidean space, provided the L^2-norm of the second fundamental form is finite. Also, by using a monotonicity formula, we prove that if the L^2-norm of mean curvature of a noncompact surface is finite, then it has at least quadratic ar…
Study on tubes with specific Gauss map properties in 3D space.
problem Characterizing surfaces with a specific Gauss map property in 3D space.
method Analyzing tubes in Euclidean 3-space with Gauss map n satisfying ΔIn = Λn.
result Circular cylinders are the only surfaces of coordinate finite I-type Gauss map.
The paper proves topological finiteness for surfaces with finite Willmore energy.
problem Understanding the topology of surfaces with finite Willmore energy.
method Combining Allard regularity theorem and Reifenberg's topological disk theorem.
result Topological finiteness for a class of properly immersed surfaces with finite Willmore energy.
We describe infinitesimal deformations of constant mean curvature surfaces of finite type in the 3-sphere. We use Baker-Akhiezer functions to describe such deformations, as well as polynomial Killing fields and the corresponding spectral curve to distinguish between isospectral and non-isospectral deformations.
We prove that there is no functorial universal finite type invariant for braids in if the genus of is positive.
New theorem for surfaces in hyperbolic and de Sitter spaces.
problem Proving a Picard type theorem for specific types of surfaces.
method Following Jorge and Mercuri's approach for minimal surfaces, extending to CMC-1 surfaces.
result Proves a similar theorem for CMC-1 surfaces in hyperbolic and de Sitter spaces.