Spinorial Yamabe Type Equations on S3 via Conley Index

DOI10.1515/ans-2015-0103zbMath1316.35249OpenAlexW2507902613MaRDI QIDQ5178515

Takeshi Isobe

Publication date: 16 March 2015

Published in: Advanced Nonlinear Studies (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ans-2015-0103

zbMATH Keywords

Conley indexcritical Sobolev exponentvariational methodspinorial Yamabe equation

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Critical points and critical submanifolds in differential topology (57R70) Index theory for dynamical systems, Morse-Conley indices (37B30) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (8)

A perturbation method for spinorial Yamabe type equations on \(S^m\) and its application ⋮ Morse-Floer theory for superquadratic Dirac equations. I: Relative Morse indices and compactness ⋮ Morse homology for asymptotically linear Dirac equations on compact manifolds ⋮ Solutions of spinorial Yamabe-type problems on 𝑆^{𝑚}: Perturbations and applications ⋮ Nonlinear Dirac equations, monotonicity formulas and Liouville theorems ⋮ A spinorial analogue of the Brezis-Nirenberg theorem involving the critical Sobolev exponent ⋮ Asymptotically linear Dirac-harmonic maps into flat tori ⋮ On the multiple existence of superquadratic Dirac-harmonic maps into flat tori

Cites Work

• Nonlinear Dirac equations with critical nonlinearities on compact spin manifolds
• The scalar-curvature problem on the standard three-dimensional sphere
• Dirac-harmonic maps
• Mass endomorphism and spinorial Yamabe type problems on conformally flat manifolds
• A Sobolev-like inequality for the Dirac operator
• The smallest Dirac eigenvalue in a spin-conformal class and cmc immersions
• The scalar curvature equation on 2- and 3-spheres
• A spin-conformal lower bound of the first positive Dirac eigenvalue
• The scalar curvature problem on \(S^n\): An approach via Morse theory
• The Cauchy problems for Einstein metrics and parallel spinors
• Nonlinear Dirac equations on Riemann surfaces
• An obstruction for the mean curvature of a conformal immersion 𝑆ⁿ→ℝⁿ⁺¹
• On the Hopf Index and the Conley Index

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