Should We Solve Plateau’s Problem Again?
Should We Solve Plateau’s Problem Again?
This chapter gives a partial account of the situation of Plateau's problem on the existence and regularity of soap films with a given boundary. It starts with a description of some of the most celebrated solutions of Plateau's problem, followed by a description of a few easy examples. The chapter then returns to the modeling problem and mentions a few additional ways to state a Plateau problem. It briefly describes the known local regularity properties of the Almgren minimal sets, and why we would like to extend some of these regularity results to sliding minimal sets, all the way to the boundary. At the same time, the chapter considers why these solutions are not always entirely satisfactory. Finally, the chapter explains why the regularity results for sliding Almgren minimal sets also apply to solutions of the Reifenberg and size minimization problems described earlier in the chapter.
Keywords: Plateau's problem, soap films, Almgren minimal sets, Reifenberg, size minimization problems, sliding minimal sets
Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.
