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National Repository of Grey Literature 1 records found  Search took 0.00 seconds. 
Minimal surfaces and their applications
 Beran, Filip ; Šír, Zbyněk (advisor) ; Slavík, Antonín (referee)
The aim of this bachelor thesis is to explain basic qualities of minimal surfaces and to demonstrate some significant examples. The first chapter summarizes clas- sic concepts of differential geometry of curves and surfaces, which are essential for formulation of the surface minimization problem. Solving of this variational problem brings us back to local property of surface, zero mean curvature. In the rest of the second chapter we reveal which other properties this condition implies; one of the most important is the conformity of the Gauss map. Emphasizing the geometric view, in the third chapter we derive minimal surfaces of revolution and ruled minimal surfaces. Finally we construct isometric deformation of these one parameter surface families, catenoids and helicoids, to show nontrivial case of local isometry which is also typical for minimal surfaces. 1
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