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Autor:
Philip L. Bowers, Kenneth Stephenson
Publikováno v:
Conformal Geometry and Dynamics of the American Mathematical Society. 23:52-104
This is the second in a series of papers on conformal tilings. The overriding themes here are local isomorphisms, hierarchical structures, and the conformal “type” problem. Conformal tilings were introduced by the authors in 1997 with a conformal
Publikováno v:
Geometriae Dedicata. 203:337-346
We verify the infinitesimal inversive rigidity of almost all triangulated circle polyhedra in the Euclidean plane $${\mathbb {E}}^{2}$$ , as well as the infinitesimal inversive rigidity of tangency circle packings on the 2-sphere $${\mathbb {S}}^{2}$
Autor:
Philip L. Bowers
Publikováno v:
In the Tradition of Thurston ISBN: 9783030559274
This chapter presents a whirlwind tour of some results surrounding the Koebe–Andre’ev–Thurston Theorem, Bill Thurston’s seminal circle packing theorem that appears in Chapter 13 of The Geometry and Topology of Three-Manifolds.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::66347569005dc1a6b66a58f02b16991d
https://doi.org/10.1007/978-3-030-55928-1_5
https://doi.org/10.1007/978-3-030-55928-1_5
Autor:
Philip L. Bowers, John C. Bowers
Publikováno v:
Discrete & Computational Geometry. 60:9-26
We present constructions inspired by the Ma–Schlenker example of “Non-rigidity of spherical inversive distance circle packings” (Discrete Comput Geom 47(3):610–617, 2012). In contrast to the use in Ma and Schlenker (2012) of an infinitesimall
Autor:
Kenneth Stephenson, Philip L. Bowers
Publikováno v:
Conformal Geometry and Dynamics of the American Mathematical Society. 21:1-63
This paper opens a new chapter in the study of planar tilings by introducing conformal tilings. These are similar to traditional tilings in that they realize abstract patterns of combinatorial polygons as concrete patterns of geometric shapes, the ti
We generalize Cauchy's celebrated theorem on the global rigidity of convex polyhedra in Euclidean $3$-space $\mathbb{E}^{3}$ to the context of circle polyhedra in the $2$-sphere $\mathbb{S}^{2}$. We prove that any two convex and proper non-unitary c-
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::30263a50d6309ddb134f0865e3f93847
http://arxiv.org/abs/1703.09338
http://arxiv.org/abs/1703.09338
Autor:
Philip L. Bowers
Publikováno v:
Bulletin of the American Mathematical Society. 46:511-525