"극소곡면"의 두 판 사이의 차이
둘러보기로 가기
검색하러 가기
Pythagoras0 (토론 | 기여) (→메모) |
Pythagoras0 (토론 | 기여) (→메모) |
||
| 3번째 줄: | 3번째 줄: | ||
* 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. | * 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. | ||
* the plane in $R^3$, helicoid, catenoid, Scherk surface, and Enneper surface | * the plane in $R^3$, helicoid, catenoid, Scherk surface, and Enneper surface | ||
| − | + | * representation formula of Enneper and Weierstrass which expresses a given minimal surface in terms of integrals involving a holomorphic function μ and a meromorphic function ν | |
==관련도서== | ==관련도서== | ||
2015년 8월 3일 (월) 21:55 판
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.
- the plane in $R^3$, helicoid, catenoid, Scherk surface, and Enneper surface
- representation formula of Enneper and Weierstrass which expresses a given minimal surface in terms of integrals involving a holomorphic function μ and a meromorphic function ν
관련도서
- Dierkes, Ulrich, Stefan Hildebrandt, Friedrich Sauvigny, Ruben Jakob, and Albrecht Küster. Minimal Surfaces. 2nd, rev. and enlarged ed. 2010 edition. Fort Worth: Springer, 2010.
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.
- 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.