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doi:10.22028/D291-35635 | Title: | Some Geometric Properties of Nonparametric $$\mu $$-Surfaces in $$\pmb {{\mathbb {R}}}^3$$ |
| Author(s): | Bildhauer, Michael Fuchs, Martin |
| Language: | English |
| Title: | The Journal of Geometric Analysis |
| Volume: | 32 |
| Issue: | 4 |
| Publisher/Platform: | Springer Nature |
| Year of Publication: | 2022 |
| Free key words: | Generalized minimal surfaces μ-Ellipticity Nonparametric surfaces Variational problems from geometry |
| DDC notations: | 510 Mathematics |
| Publikation type: | Journal Article |
| Abstract: | Smooth solutions of the equation div g |∇u| |∇u| ∇u = 0 are considered generating nonparametric μ-surfaces in R3, whenever g is a function of linear growth satisfying in addition ∞ 0 sg (s)ds < ∞. Particular examples are μ-elliptic energy densities g with exponent μ > 2 (see Bild hauer and Fuchs in Rend Mat Appl 22(7):249–274, 2003) and the minimal surfaces belong to the class of 3-surfaces. Generalizing the minimal surface case we prove the closedness of a suitable differential form Nˆ ∧dX. As a corollary we find an asymptotic conformal parametrization generated by this differential form. |
| DOI of the first publication: | 10.1007/s12220-021-00819-6 |
| Link to this record: | urn:nbn:de:bsz:291--ds-356359 hdl:20.500.11880/32510 http://dx.doi.org/10.22028/D291-35635 |
| ISSN: | 1559-002X 1050-6926 |
| Date of registration: | 2-Mar-2022 |
| Faculty: | MI - Fakultät für Mathematik und Informatik |
| Department: | MI - Mathematik |
| Professorship: | MI - Prof. Dr. Martin Fuchs |
| Collections: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
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| File | Description | Size | Format | |
|---|---|---|---|---|
| Bildhauer-Fuchs2022_Article_SomeGeometricPropertiesOfNonpa.pdf | 337,95 kB | Adobe PDF | View/Open |
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