Conformal Dirac-Einstein equations on manifolds with boundary.

DOI10.1007/s00526-022-02354-wOpenAlexW4308267337WikidataQ115385844 ScholiaQ115385844MaRDI QIDQ2093436

Vittorio Martino, William Borrelli, Ali Maalaoui

Publication date: 8 November 2022

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.00031

Mathematics Subject Classification ID

Variational principles in infinite-dimensional spaces (58E30) Spin and Spin({}^c) geometry (53C27) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A spinorial energy functional: critical points and gradient flow
• Rabinowitz-Floer homology for superquadratic Dirac equations on compact spin manifolds
• The boundary value problem for the super-Liouville equation
• A positive mass theorem for asymptotically flat manifolds with a non-compact boundary
• Nonlinear Dirac equations with critical nonlinearities on compact spin manifolds
• Homological approach to problems with jumping non-linearity
• Energy identities and blow-up analysis for solutions of the super Liouville equation
• Periodic nonlinear Schrödinger equation with application to photonic crystals
• The Rabinowitz-Floer homology for a class of semilinear problems and applications
• On a spin conformal invariant on manifolds with boundary
• The Dirac spectrum
• Spineurs, opérateurs de Dirac et variations de métriques. (Spinors, Dirac operators and variations of the metrics)
• The Yamabe problem on manifolds with boundary
• On the proof of the positive mass conjecture in general relativity
• The positive mass theorem for black holes revisited
• On the spectrum of the Dirac operator under boundary conditions
• A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds
• A new proof of the positive energy theorem.
• Super-Liouville theory with boundary
• Estimates for solutions of Dirac equations and an application to a geometric elliptic-parabolic problem
• Generalized cylinders in semi-Riemannian and spin geometry
• Harmonic spinors
• Eigenvalue boundary problems for the Dirac operator
• The Einstein-Dirac equation on Riemannian spin manifolds
• Some properties of Dirac-Einstein bubbles
• Compactness of Dirac-Einstein spin manifolds and horizontal deformations
• A positive mass theorem for manifolds with boundary
• Energy quantization for a singular super-Liouville boundary value problem
• The Calderón-Zygmund inequality and Sobolev spaces on noncompact Riemannian manifolds
• Characterization of the Palais-Smale sequences for the conformal Dirac-Einstein problem and applications
• The qualitative boundary behavior of blow-up solutions of the super-Liouville equations
• The Hijazi inequality on manifolds with boundary
• Ground state Dirac bubbles and Killing spinors
• Existence results for the conformal Dirac-Einstein system
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Killing vectors in asymptotically flat space-times. II. Asymptotically translational Killing vectors and the rigid positive energy theorem in higher dimensions
• The Yamabe problem
• Spectral asymmetry and Riemannian Geometry. I
• Boundary value problems for Dirac-type equations
• Existence Results for Super-Liouville Equations on the Sphere via Bifurcation Theory
• Existence results for a super-Liouville equation on compact surfaces
• Riemannian geometry and geometric analysis
• The Einstein-Dirac equation on Sasakian 3-manifolds.