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.

UR - http://www.scopus.com/inward/record.url?scp=85043990138&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043990138&partnerID=8YFLogxK

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 -