Let ~ and ]~ be positive solutions on (0, ~) to the rotationally symmetric p-harmonic map equation on model manifolds M(f) and M(ff), where f is assumed to he sufficiently large near infinity and g"(y) >1 0 for y>0. We show that if and fl have the same limit at infinity, then ~ -]~ on (0, o<~).
โฆ LIBER โฆ
Rotationally symmetric 1-harmonic maps fromD2toS2
โ Scribed by Roberta Dal Passo; Lorenzo Giacomelli; Salvador Moll
- Publisher
- Springer
- Year
- 2008
- Tongue
- English
- Weight
- 377 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0944-2669
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We study a second order ordinary differential equation which is the EulerLagrange equation of the energy functional for maps with prescribed rotational symmetry. We obtain Liouville's type theorems for symmetric harmonic maps into ellipsoids, Euclidean and Hyperbolic spaces, and existence results as