Liouville-type results for stationary maps of a class of functional related to pullback metrics
| Autor: | Said Asserda |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Mathematics - Differential Geometry
Comparison theorem Pure mathematics Applied Mathematics Riemannian geometry First variation symbols.namesake Mathematics - Analysis of PDEs Primary 58E20 Secondary 53C21 Differential Geometry (math.DG) Pullback Tensor (intrinsic definition) FOS: Mathematics symbols Stress–energy tensor Coarea formula Boundary value problem Analysis Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Nonlinear Analysis: Theory, Methods & Applications. 75:3480-3492 |
| ISSN: | 0362-546X |
| DOI: | 10.1016/j.na.2012.01.005 |
| Popis: | We study a generalized functional related to the pullback metrics (3). We derive the first variation formula which yield stationary maps. We introduce the stress–energy tensor which is naturally linked to conservation law and yield the monotonicity formula via the coarea formula and the comparison theorem in Riemannian geometry. A version of this monotonicity inequalities enables us to derive some Liouville type results. Also, we investigate the constant Dirichlet boundary value problems and the generalized Chern type results for tension field equation with respect to this functional. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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