publication . Article . Preprint . 2017

Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds II : Morse Theory

Ikoma, Norihisa; Malchiodi, Andrea; Mondino, Andrea;
Open Access English
  • Published: 01 Oct 2017
  • Publisher: The Johns Hopkins University Press
  • Country: United Kingdom
Comment: Final version, to appear in the American Journal of Mathematics
arXiv: Mathematics::Differential GeometryMathematics::Symplectic Geometry
free text keywords: QA, Mathematics - Differential Geometry, Mathematics - Analysis of PDEs, Mathematics - Algebraic Topology, 49Q10, 53C21, 53C42, 35J60, 83C99, Manifold, Curvature, Degenerate energy levels, Normal coordinates, Morse theory, Torus, Geodesic, Tensor, Topology, Mathematics, Mathematical analysis
20 references, page 1 of 2

[1] A. Ambrosetti, M. Badiale, Homoclinics: Poincar´e-Melnikov type results via a variational approach, Ann. Inst. Henri Poincar´e Analyse Non Lin`eaire 15, (1998), 233-252 . [OpenAIRE]

[2] A. Ambrosetti, M. Badiale, Variational perturbative methods and bifurcation of bound states from the essential spectrum Proc. R. Soc. Edinb. 18, (1998), 1131-1161.

[4] M. Barros, A. Ferr´andez, P. Lucas, M. A. Merono, Willmore tori and Willmore-Chen submanifolds in pseudo-Riemannian spaces, J. Geom. Phys., Vol. 28, (1998), 45-66.

[14] E. Kuwert, A. Mondino, J. Schygulla, Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds, Math. Ann. Vol. 359, Num. 1-2, 379-425, (2014). [OpenAIRE]

[15] E. Kuwert, R. Scha¨tzle, Removability of isolated singularities of Willmore surfaces, Annals of Math. Vol. 160, Num. 1, (2004), 315-357. [OpenAIRE]

[16] T. Lamm, J. Metzger, Small surfaces of Willmore type in Riemannian manifolds, Int. Math. Res. Not. 19 (2010), 3786-3813.

[17] T. Lamm, J. Metzger, Minimizers of the Willmore functional with a small area constraint, Annales IHP-Anal. Non Lin., Vol. 30, (2013), 497-518.

[18] T. Lamm, J. Metzger, F. Schulze, Foliations of asymptotically flat manifolds by surfaces of Willmore type, Math. Ann., Vol. 350, Num. 1, (2011), 1-78.

[19] P. Laurain, A. Mondino, Concentration of small Willmore spheres in Riemannian 3-manifolds, preprint arXiv:1310.7082 (2013), accepted for publication in Analysis & PDE.

[20] J. M. Lee, T. H. Parker, The Yamabe problem, Bull. Amer. Math. Soc. (N.S.), Vol. 17, Num. 1, (1987), 37-91.

[21] P. Li, S. T. Yau, A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces, Invent. Math., Vol. 69, Num. 2, (1982), 269-291.

[22] F. Marques, A. Neves, Min-max theory and the Willmore conjecture, Annals of Math., Vol. 179, Num. 2, (2014), 683-782.

[33] T. Rivi`ere, Analysis aspects of Willmore surfaces, Invent. Math., Vol. 174, Num. 1, (2008), 1-45.

[34] T. Rivi`ere, Variational Principles for immersed Surfaces with L2-bounded Second Fundamental Form, arXiv:1007.2997, preprint (2010), J. Reine. Angew. Math. (in press).

[35] A. Ros, The Willmore conjecture in the real projective space, Math. Res. Lett., Vol. 6, (1999), 487- 493.

20 references, page 1 of 2
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue