Minimalne ploskve

delo diplomskega seminarja

Katarina Gačnik (Author), Uroš Kuzman (Mentor)

Abstract

V delu diplomskega seminarja obravnavamo minimalne ploskve. To je, dvodimenzionalne objekte, katerih površina je lokalno minimalna. S pomočjo variacijskega računa bomo izpeljali Euler-Lagrangeovo parcialno diferencialno enačbo, ki ji mora zadoščati vsaka eksplicitno podana minimalna ploskev. Nadalje bomo pokazali, da je parametrično podana ploskev minimalna natanko tedaj, ko ima ničelno srednjo ukrivljenost. Nazadnje si bomo ogledali še primer, ki potrdi, da minimalne ploskve niso nujno tudi globalno ekstremne. To pomeni, da lahko pri danih robnih pogojih najdemo več minimalnih ploskev z različnimi površinami.

Keywords

matematika;minimalne ploskve;lokalni minimum;globalni minimum;variacijski račun;diferencialna geometrija;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[K. Gačnik]
UDC:	514.7
COBISS:	18411865
Views:	937
Downloads:	490
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Minimal surfaces
Secondary abstract:	In this dissertation we study minimal surfaces. That is, two-dimensional objects whose area is locally minimal. Using the calculus of variations we will derive the Euler-Lagrange differential equation which has to be fulfilled for explicitly given minimal surfaces. Further, we will show that a parametric surface is minimal if and only if its mean curvature equals zero. Finally, we will present an example which points out that a minimal surface is not always a global extreme. This means that, given boundary conditions, there may exist several minimal surfaces with different areas.
Secondary keywords:	mathematics;minimal surfaces;local minimum;global minimum;calculus of variations;differential geometry;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages:	23 str.
ID:	10949234