TY - GEN
T1 - Trivalent Maximal Surfaces in Minkowski Space
AU - Lam, Wai Yeung
AU - Yasumoto, Masashi
N1 - Funding Information:
Acknowledgements The second author was supported by 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:
© Springer International Publishing AG 2017.
PY - 2017
Y1 - 2017
N2 - We investigate discretizations of maximal surfaces in Minkowski space, which are surfaces with vanishing mean curvature. The corresponding discrete surfaces admit a Weierstrass-type representation in terms of discrete holomorphic quadratic differentials. There are two particular types of discrete maximal surfaces that are obtained by taking the real part and the imaginary part of the representation formula, and they are deformable to each other by a one-parameter family. We further introduce a compatible notion of vertex normals for general trivalent surfaces to characterize their singularities in Minkowski space as in the smooth theory.
AB - We investigate discretizations of maximal surfaces in Minkowski space, which are surfaces with vanishing mean curvature. The corresponding discrete surfaces admit a Weierstrass-type representation in terms of discrete holomorphic quadratic differentials. There are two particular types of discrete maximal surfaces that are obtained by taking the real part and the imaginary part of the representation formula, and they are deformable to each other by a one-parameter family. We further introduce a compatible notion of vertex normals for general trivalent surfaces to characterize their singularities in Minkowski space as in the smooth theory.
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U2 - 10.1007/978-3-319-66290-9_10
DO - 10.1007/978-3-319-66290-9_10
M3 - Conference contribution
AN - SCOPUS:85043990138
SN - 9783319662893
T3 - Springer Proceedings in Mathematics and Statistics
SP - 169
EP - 184
BT - Lorentzian Geometry and Related Topics - GeLoMa 2016
A2 - Canadas-Pinedo, María A.
A2 - Palomo, Francisco J.
A2 - Flores, Jose Luis
PB - Springer New York LLC
T2 - 8th International Meeting on Lorentzian Geometry,GeLoMa 2016
Y2 - 20 September 2016 through 23 September 2016
ER -