"극소곡면"의 두 판 사이의 차이

2015년 8월 3일 (월) 21:48 판

This was first considered by Lagrange (1762), who raised the question of existence of surfaces of least area having a given closed curve in three-space as the boundary. He derived the differential equation that must be satisfied by a function of two variables whose graph minimizes area among surfaces with a given contour.
Later Meusnier discovered that this is equivalent to the vanishing of the mean curvature, and the study of the differential geometry of these surfaces was started.

Jiang, YuePing, ZhiHong Liu, and Saminathan Ponnusamy. “Univalent Harmonic Mappings and Lift to the Minimal Surfaces.” arXiv:1508.00199 [math], August 2, 2015. http://arxiv.org/abs/1508.00199.
Hoffman, David, Martin Traizet, and Brian White. “Helicoidal Minimal Surfaces of Prescribed Genus.” arXiv:1508.00064 [math], July 31, 2015. http://arxiv.org/abs/1508.00064.
Marques, Fernando Coda. “Minimal Surfaces - Variational Theory and Applications.” arXiv:1409.7648 [math], September 26, 2014. http://arxiv.org/abs/1409.7648.
Gutshabash, E. Sh. “Nonlinear Sigma Model, Zakharov-Shabat Method, and New Exact Forms of the Minimal Surfaces in $R^3$.” arXiv:1409.6741 [math-Ph, Physics:nlin], September 23, 2014. http://arxiv.org/abs/1409.6741.

@@ 1번째 줄: / 1번째 줄: @@
+==메모==
+* This was first considered by Lagrange (1762), who raised the question of existence of surfaces of least area having a given closed curve in three-space as the boundary. He derived the differential equation that must be satisfied by a function of two variables whose graph minimizes area among surfaces with a given contour.
+* Later Meusnier discovered that this is equivalent to the vanishing of the mean curvature, and the study of the differential geometry of these surfaces was started.
 ==관련논문==
 * Jiang, YuePing, ZhiHong Liu, and Saminathan Ponnusamy. “Univalent Harmonic Mappings and Lift to the Minimal Surfaces.” arXiv:1508.00199 [math], August 2, 2015. http://arxiv.org/abs/1508.00199.