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Minimalne ploskve : delo diplomskega seminarja
ID Gačnik, Katarina (Author), ID Kuzman, Uroš (Mentor) More about this mentor... This link opens in a new window

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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.

Language:Slovenian
Keywords:minimalne ploskve, lokalni in globalni minimum, variacijski račun, diferencialna geometrija
Work type:Final seminar paper
Typology:2.11 - Undergraduate Thesis
Organization:FMF - Faculty of Mathematics and Physics
Year:2018
PID:20.500.12556/RUL-102146 This link opens in a new window
UDC:514.7
COBISS.SI-ID:18411865 This link opens in a new window
Publication date in RUL:20.07.2018
Views:1455
Downloads:559
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Secondary language

Language:English
Title:Minimal surfaces
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.

Keywords:minimal surfaces, local and global minimum, calculus of variations, differential geometry

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