Zobrazeno 1 - 10
of 66
pro vyhledávání: '"WANG, Erxiao"'
Convex hexagons that can tile the plane have been classified into three types. For the generic cases (not necessarily convex) of the three types and two other special cases, we classify tilings of the plane under the assumption that all vertices have
Externí odkaz:
http://arxiv.org/abs/2405.04843
Autor:
Yuan, Qi, Wang, Erxiao
All edge-to-edge tilings of the sphere by congruent regular triangles and congruent rhombi are classified as: (1) a $1$-parameter family of protosets each admitting a unique $(2a^3,3a^4)$-tiling like a triangular prism; (2) a $1$-parameter family of
Externí odkaz:
http://arxiv.org/abs/2311.01183
Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This last one classifies the case of $a^3b$-quadrilaterals with some irrational angle: there are a sequence of $1$-parameter familie
Externí odkaz:
http://arxiv.org/abs/2206.15342
Autor:
Liao, Yixi, Wang, Erxiao
Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Diophantine equations to classify the case of $a^3b$-quadrilaterals with
Externí odkaz:
http://arxiv.org/abs/2205.14936
The edge-to-edge tilings of the sphere by congruent quadrilaterals of Type $a^2bc$ are classified as $3$ classes: a sequence of two-parameter families of $2$-layer earth map tilings with $2n$ $(n\ge3)$ tiles, a one-parameter family of quadrilateral s
Externí odkaz:
http://arxiv.org/abs/2110.10087
Pentagonal subdivision gives three families of edge-to-edge tilings of the sphere by congruent pentagons. Each family forms a two dimensional moduli. We describe the moduli in detail.
Comment: 39 pages, 22 figures
Comment: 39 pages, 22 figures
Externí odkaz:
http://arxiv.org/abs/1907.08776
Autor:
Wang, Erxiao, Yan, Min
There are fifteen edge-to-edge tilings of the sphere by congruent pentagons with the edge combination $a^3b^2$: five one-parameter families of pentagonal subdivision tilings, and ten flip modifications of three special cases of two pentagonal subdivi
Externí odkaz:
http://arxiv.org/abs/1903.02712
The classical result of describing harmonic maps from surfaces into symmetric spaces of reductive Lie groups states that the Maurer-Cartan form with an additional parameter, the so-called loop parameter, is integrable for all values of the loop param
Externí odkaz:
http://arxiv.org/abs/1902.01558
Publikováno v:
J. Inst. Math. Jussieu 21 (2022) 459-485
Rational loops played a central role in Uhlenbeck's construction of harmonic maps into U(n) (chiral model in physics), and they are generated by simple elements with one pole and one zero constructed from Hermitian projections. It has been believed f
Externí odkaz:
http://arxiv.org/abs/1812.01456
There are exactly eight edge-to-edge tilings of the sphere by congruent equilateral pentagons: three pentagonal subdivision tilings with 12, 24, 60 tiles; four earth map tilings with 16, 20, 24, 24 tiles; and one flip modification of the earth map ti
Externí odkaz:
http://arxiv.org/abs/1805.07217