Abstract
AbstractGiven a closed manifold of dimension at least three, with non-trivial homotopy group $$\pi _3(M)$$
π
3
(
M
)
and a generic metric, we prove that there is a finite collection of harmonic spheres with Morse index bounded by one, with sum of their energies realizing a geometric invariant width.
Publisher
Springer Science and Business Media LLC
Reference22 articles.
1. Colding, T.H., Minicozzi, W.P.: II. Width and finite extinction time of Ricci flow. Geom. Topol. 12(5), 2537–2586 (2008)
2. Colding, T.H., Minicozzi, W.P.: II. A Course in Minimal Surfaces. Volume 121 of Graduate Studies in Mathematics. American Mathematical Society, Providence (2011)
3. Choi, H.I., Schoen, R.: The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature. Invent. Math. 81(3), 387–394 (1985)
4. Chen, J., Tian, G.: Compactification of moduli space of harmonic mappings. Comment. Math. Helv. 74(2), 201–237 (1999)
5. Ejiri, N., Micallef, M.: Comparison between second variation of area and second variation of energy of a minimal surface. Adv. Calc. Var. 1(3), 223–239 (2008)