TY - JOUR
T1 - Construction of discrete constant mean curvature surfaces in Riemannian spaceforms and applications
AU - Ogata, Yuta
AU - Yasumoto, Masashi
N1 - Funding Information:
The authors would like to thank Wayne Rossman, Tim Hoffmann, Udo Hertrich-Jeromin, Fran Burstall, Pascal Romon, Christoph Bohle and Wolfgang Carl for helpful discussions and valuable comments. In particular, while the authors were writing this paper, they knew that Bobenko and Romon [5] were working on similar problems. The authors are grateful to Pascal Romon for sharing the problems treated in [5] . The second author was supported by the Grant-in-Aid for JSPS Fellows Number 26-3154 , JSPS/FWF bilateral joint project “Transformations and Singularities” between Austria and Japan, and the JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers “Mathematical Science of Symmetry, Topology and Moduli, Evolution of International Research Network based on OCAMI”.
Funding Information:
The authors would like to thank Wayne Rossman, Tim Hoffmann, Udo Hertrich-Jeromin, Fran Burstall, Pascal Romon, Christoph Bohle and Wolfgang Carl for helpful discussions and valuable comments. In particular, while the authors were writing this paper, they knew that Bobenko and Romon [5] were working on similar problems. The authors are grateful to Pascal Romon for sharing the problems treated in [5]. The second author was supported by the Grant-in-Aid for JSPS Fellows Number 26-3154, JSPS/FWF bilateral joint project “Transformations and Singularities” between Austria and Japan, and the JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers “Mathematical Science of Symmetry, Topology and Moduli, Evolution of International Research Network based on OCAMI”.
Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2017/10
Y1 - 2017/10
N2 - In this paper we give a construction for discrete constant mean curvature surfaces in Riemannian spaceforms in terms of integrable systems techniques, which we call the discrete DPW method for discrete constant mean curvature surfaces. Using this construction, we give several examples, and analyze singularities of the parallel constant Gaussian curvature surfaces.
AB - In this paper we give a construction for discrete constant mean curvature surfaces in Riemannian spaceforms in terms of integrable systems techniques, which we call the discrete DPW method for discrete constant mean curvature surfaces. Using this construction, we give several examples, and analyze singularities of the parallel constant Gaussian curvature surfaces.
UR - http://www.scopus.com/inward/record.url?scp=85019571785&partnerID=8YFLogxK
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U2 - 10.1016/j.difgeo.2017.04.010
DO - 10.1016/j.difgeo.2017.04.010
M3 - Article
AN - SCOPUS:85019571785
SN - 0926-2245
VL - 54
SP - 264
EP - 281
JO - Differential Geometry and its Application
JF - Differential Geometry and its Application
ER -