Abstract
This chapter is centered on the proof of existence theorems for minimal surfaces with completely free boundaries. The problem is approached by applying the direct methods of the calculus of variations, thus establishing the existence of minimizers with a boundary on a given supporting surface S. However, this method does not yield the existence of stationary minimal surfaces which are not area minimizing. The remaining part of the chapter deals with additional properties of minimal surfaces with free boundaries. For instance, such a surface has to intersect the free boundary surface perpendicularly and in a balanced way. This fact implies nonexistence in certain cases. Finally an extensive report on the existence of stationary minimal surfaces with free or partially free boundaries is given.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Dierkes, U., Hildebrandt, S., Tromba, A.J. (2010). Minimal Surfaces with Free Boundaries. In: Regularity of Minimal Surfaces. Grundlehren der mathematischen Wissenschaften, vol 340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11700-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-11700-8_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11699-5
Online ISBN: 978-3-642-11700-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)