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Representing planar domains by polar parameterizations with parabolic parameter lines

Sofia Trautner, Bert Jüttler, Myung-Soo Kim
2021 Computer Aided Geometric Design  
Recently, the flexibility of these polar parameterizations has been enhanced by considering so-called arc fibrations (Jüttler et al., 2019) , which are polar parameterizations that use circular arcs in  ...  We propose and analyze another generalization of polar parameterizations, which uses parabolic arcs instead of lines or circular arcs.  ...  Conclusion Polar parameterizations of planar domains with parabolic parameter lines form a potentially useful generalization of the arc fibrations that were studied by Jüttler et al. (2019) .  ... 
doi:10.1016/j.cagd.2021.101966 fatcat:te547som4jb3vaowrtjhjnveqi

Generalizations of planar contact manifolds to higher dimensions [article]

Bahar Acu, John B. Etnyre, Burak Ozbagci
2020 arXiv   pre-print
Iterated planar contact manifolds are a generalization of three dimensional planar contact manifolds to higher dimensions.  ...  We also observe that for any odd integer m > 3, any finitely presented group can be realized as the fundamental group of some iterated planar contact manifold of dimension m.  ...  This process, of course, can be iterated as many times as desired. Note that an iterated planar Lefschetz fibration on a 4-dimensional Liouville domain is nothing but a planar Lefschetz fibration.  ... 
arXiv:2006.02940v1 fatcat:nwukcem3hzcuvp4cyuxtlml5su

Lefschetz fibrations over the disc

Nikos Apostolakis, Riccardo Piergallini, Daniele Zuddas
2013 Proceedings of the London Mathematical Society  
We provide a complete set of moves relating any two Lefschetz fibrations over the disk having as their total space the same 4-dimensional 2-handlebody up to 2-equivalence.  ...  By [15] , these fibrations represent compact Stein domains with strictly pseudoconvex boundary up to orientation-preserving diffeomorphisms.  ...  Let f : W → B 2 be a Lefschetz fibration with regular fibre F such that Bd F = ∅, a ⊂ F be a proper smooth arc and G ⊂ F be a regular neighbourhood of a.  ... 
doi:10.1112/plms/pds078 fatcat:ba7enicx2bby3lltr4542isjny

Constant spacing in filament bundles [article]

Daria W. Atkinson, Christian D. Santangelo, Gregory M. Grason
2019 arXiv   pre-print
The relative shapes and configurations of curves in these families are highly constrained: they must be either (isometric) developable domains, which can bend, but not twist; or (non-isometric) constant-pitch  ...  upper bounds on the growth of longitudinal variations of spacing with bundle thickness.  ...  Kusner and participants of the "Packing of Continua" workshop at the Aspen Center for Physics (NSF PHY 1607611) for numerous helpful discussions. We also thank D. Hall and H.  ... 
arXiv:1902.06325v1 fatcat:fbsrbzeponbyti5hxxixxnhw6a

Constant spacing in filament bundles

Daria W. Atkinson, Christian Santangelo, Gregory Grason
2019 New Journal of Physics  
The relative shapes and configurations of curves in these families are highly constrained: they must be either (isometric) developable domains, which can bend, but not twist; or (non-isometric) constant-pitch  ...  upper bounds on the growth of longitudinal variations of spacing with bundle thickness.  ...  Acknowledgments We are grateful to R Kusner and participants of the 'Packing of Continua' workshop at the Aspen Center for Physics (NSF PHY 1607611) for numerous helpful discussions.  ... 
doi:10.1088/1367-2630/ab1c2d fatcat:bczusawmaveefbch3ktysz54ni

Braiding link cobordisms and non-ribbon surfaces

Mark C Hughes
2015 Algebraic and Geometric Topology  
We mention several applications of braided surfaces with caps, including using them to apply algebraic techniques from braid groups to studying surfaces in 4-space, as well as constructing singular fibrations  ...  These surfaces are closely related to another notion of surface braiding in D^2 × D^2, called braided surfaces with caps, which are a generalization of Rudolph's braided surfaces.  ...  arc.  ... 
doi:10.2140/agt.2015.15.3707 fatcat:xp2242fo2fhahdny3urzr2gfey

Shape Analysis: Euclidean, Discrete and Algebraic Geometric Methods (Dagstuhl Seminar 18422)

Michael Breuß, Alfred M. Bruckstein, Christer Oscar Kiselman, Petros Maragos, Michael Wagner
2019 Dagstuhl Reports  
In computer vision, geometric processing and image analysis, the notation of a shape of a 3-D object has been studied either by an embedded manifold for the continuous stetting or as a collection of a  ...  discrete set of marker positions on the manifold.  ...  Parameterizations that are regular everywhere except at the center are said to form an arc fibration of a planar domain.  ... 
doi:10.4230/dagrep.8.10.87 dblp:journals/dagstuhl-reports/BreussBKM18 fatcat:qzsc5ihgsfhzlmooaukqjo2rcy

Contact surgery on the Hopf link: classification of fillings [article]

Edoardo Fossati
2020 arXiv   pre-print
We classify its minimal symplectic fillings up to homeomorphism (and often up to diffeomoprhism), extending the results of Lisca which covers the case of universally tight structures and the article of  ...  Plamenevskaya - Van Horn Morris which describes the fillings of L(p,1).  ...  has a Stein structure on its total space, and, vice versa, any Stein domain can be given such a fibration structure.  ... 
arXiv:1905.13026v3 fatcat:lcljk3fthjby3pxagcnqcjz2ey

Bounds on Multiplicities of Laplace Operator Eigenvalues on Surfaces [article]

Aleksandr Berdnikov
2015 arXiv   pre-print
In the present paper several bounds on multiplicities of eigenvalues of the Laplacian operator on surfaces are generalized from the case of either closed surface or simply-connected planar domain to the  ...  case of a surface of positive genus with holes.  ...  planar domains with the Dirichlet boundary condition.  ... 
arXiv:1511.09043v1 fatcat:ksmgoxkfcnfhtb5vkba5uddkva

The `Holiverse': holistic eversion of the 2-sphere in ^3 [article]

Iain R. Aitchison
2010 arXiv   pre-print
Ingredients of this eversion are seamlessly connected. We also give the mathematical origins of the proof: the Hopf fibration, and the topological structure of real-projective 3-space.  ...  We give a short, simple and conceptual proof, based on spin structures, of sphere eversion: an embedded 2-sphere in R^3 can be turned inside out by regular homotopy.  ...  The author would like to express thanks to Professor Makoto Sakuma and Professor George Francis for their very helpful suggestions, and members of the Department of Mathematics at Hiroshima University  ... 
arXiv:1008.0916v1 fatcat:2aismivrrbhs7npbvgmzyivrlq

Surface singularities and planar contact structures [article]

Paolo Ghiggini, Marco Golla, Olga Plamenevskaya
2020 arXiv   pre-print
Additionally, we prove that every finitely presented group is the fundamental group of a Lefschetz fibration with planar fibers.  ...  Applying these obstructions to canonical contact structures on links of normal surface singularities, we show that links of isolated singularities of surfaces in the complex 3-space are planar only in  ...  Let φ be the product of positive Dehn twists along α 1 , . . . , α n−d . By construction, the associated Lefschetz fibration W is a Stein domain whose fundamental group is precisely G.  ... 
arXiv:1708.04108v4 fatcat:v6gh5exd2rdppephjmrtde5lmm

Surface singularities and planar contact structures

Paolo Ghiggini, Marco Golla, Olga Plamenevskaya
2021 Annales de l'Institut Fourier  
Additionally, we prove that every finitely presented group is the fundamental group of a Lefschetz fibration with planar fibers. Résumé.  ...  Applying these obstructions to canonical contact structures on links of normal surface singularities, we show that links of isolated singularities of surfaces in the complex 3-space are planar only in  ...  We can assume that the 2-handles are attached to fibers of P × D over points in a small arc in ∂D .  ... 
doi:10.5802/aif.3384 fatcat:weggqxtoqrhgzm6ryxsef2qr7i

Families of contact 3-manifolds with arbitrarily large Stein fillings

R. Inanç Baykur, Jeremy Van Horn-Morris, Samuel Lisi, Chris Wendl
2015 Journal of differential geometry  
To produce our examples, we set a framework which generalizes the construction of Stein structures on allowable Lefschetz fibrations over the 2-disk to those over any orientable base surface, along with  ...  disproves a conjecture of Stipsicz and Ozbagci.  ...  Following the works of Eliashberg and Gompf on handle decompositions of compact Stein manifolds, Loi and Piergallini, proved that any Stein domain admits a Lefschetz fibration structure [25] (and an  ... 
doi:10.4310/jdg/1445518920 fatcat:2bfggsn3fndbphtcv7ipzs3sea

Families of contact 3-manifolds with arbitrarily large Stein fillings [article]

R. Inanc Baykur, Jeremy Van Horn-Morris
2012 arXiv   pre-print
To produce our examples, we set a framework which generalizes the construction of Stein structures on allowable Lefschetz fibrations over the 2-disk to those over any orientable base surface, along with  ...  disproves a conjecture of Stipsicz and Ozbagci.  ...  Following the works of Eliashberg and Gompf on handle decompositions of compact Stein manifolds, Loi and Piergallini, proved that any Stein domain admits a Lefschetz fibration structure [25] (and an  ... 
arXiv:1208.0528v1 fatcat:iuo6533cnregbi6xzvfow3xcju

Equivalent characterizations of handle-ribbon knots [article]

Maggie Miller, Alexander Zupan
2020 arXiv   pre-print
theorem of Casson and Gordon to the non-fibered case for handle-ribbon knots.  ...  We also show that K bounds a handle-ribbon disk D ⊂ B if and only if the 3-manifold obtained by zero-surgery on K admits a singular fibration that extends over handlebodies in B ∖ D, generalizing a classical  ...  ij , where k + 1 ≤ i, j ≤ g, we can extend Q by introducing a fold arc with a single cusp, which has no effect on the topology of the domain but modifies the range to be (I × [0, 1/3]) ∪ ([1/2, 1] × [1  ... 
arXiv:2005.11243v1 fatcat:xafko2fayvenpjfmaozvd23gni
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