Solutions of spinorial Yamabe-type problems on 𝑆^{𝑚}: Perturbations and applications

DOI10.1090/tran/8961arXiv2304.02807OpenAlexW4366403964MaRDI QIDQ6135838

Tian Xu, Takeshi Isobe

Publication date: 28 August 2023

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2304.02807

zbMATH Keywords

perturbation methodDirac operatorconformal classspinorial Yamabe equation

Mathematics Subject Classification ID

Applications of PDEs on manifolds (58J90) Spin and Spin({}^c) geometry (53C27) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Perturbations of PDEs on manifolds; asymptotics (58J37) PDEs on manifolds (35R01)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds
• Mass endomorphism, surgery and perturbations
• Infinitely many solutions for the spinorial Yamabe problem on the round sphere
• Nonlinear Dirac equations with critical nonlinearities on compact spin manifolds
• The scalar-curvature problem on the standard three-dimensional sphere
• Perturbation methods and semilinear elliptic problems on \(\mathbb R^n\)
• Generic metrics and the mass endomorphism on spin three-manifolds
• Mass endomorphism and spinorial Yamabe type problems on conformally flat manifolds
• A spinorial analogue of Aubin's inequality
• A Sobolev-like inequality for the Dirac operator
• The Dirac spectrum
• The smallest Dirac eigenvalue in a spin-conformal class and cmc immersions
• A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors
• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
• A perturbation result in prescribing scalar curvature on \(S^ n\)
• Critical point theory and Hamiltonian systems
• Differential geometry in the large. Seminar lectures New York University 1946 and Stanford University 1956. With a preface by S. S. Chern.
• Spineurs, opérateurs de Dirac et variations de métriques. (Spinors, Dirac operators and variations of the metrics)
• Weierstrass formula for surfaces of prescribed mean curvature
• On the spinor representation of surfaces in Euclidean \(3\)-space
• Perturbation of \(\Delta u+u^{(N+2)/(N-2)}=0\), the scalar curvature problem in \(\mathbb{R}^N\), and related topics
• The scalar curvature equation on 2- and 3-spheres
• Homoclinics: Poincaré-Melnikov type results via a variational approach
• The scalar curvature problem on \(S^n\): An approach via Morse theory
• Infinite dimensional Morse theory and multiple solution problems
• Harmonic spinors
• A multiplicity result for the Yamabe problem on \(S^n\)
• The Weierstrass representation of closed surfaces in \(\mathbb{R}^3\)
• A perturbation method for spinorial Yamabe type equations on \(S^m\) and its application
• Variational perturbative methods and bifurcation of bound states from the essential spectrum
• IMMERSION ANOMALY OF DIRAC OPERATOR ON SURFACE IN ℝ³
• Modified Novikov--Veselov equation and differential geometry of surfaces
• Induced Surfaces and Their Integrable Dynamics
• Spinorial Yamabe Type Equations on S³ via Conley Index
• Uniqueness theorems for surfaces in the large. I, II, III, IV, V
• A variational analysis of the spinorial Yamabe equation on product manifolds

This page was built for publication: Solutions of spinorial Yamabe-type problems on 𝑆^{𝑚}: Perturbations and applications