35 citations · 60 across the 11 of their papers we have counts for
12 papers
Non-compactness results for the spinorial Yamabe-type problems with non-smooth geometric data
Takeshi Isobe, Yannick Sire, Tian Xu
Let be an -dimensional closed spin manifold, with a fixed Riemannian metric and a fixed spin structure ; let be the spinor bun…
Solutions of Spinorial Yamabe-type Problems on : Perturbations and Applications
Takeshi Isobe, Tian Xu
This paper is part of a program to establish the existence theory for the conformally invariant Dirac equation \[ D_{\textit{g}}ψ=f(x)|ψ|_{\textit{g}}^{\frac2{m-1}}ψ\] on a closed…
Curvature effect in the spinorial Yamabe problem on product manifolds
Thomas Bartsch, Tian Xu
Let , be closed Riemannian spin manifolds. We study the existence of solutions of the spinorial Yamabe problem on the product $M_1\…
Constructions of Delaunay-type solutions for the spinorial Yamabe equation on spheres
Ali Maalaoui, Yannick Sire, Tian Xu
In this paper we construct singular solutions to the critical Dirac equation on spheres. More precisely, first we construct solutions admitting two points singularities that we cal…
On the Bär-Hijazi-Lott invariant for the Dirac operator and a spinorial proof of the Yamabe problem
Yannick Sire, Tian Xu
Let be a closed spin manifold of dimension equipped with a Riemannian metric $\ig$ and a spin structure $\sa$. Let $\lm_1^+(\tilde\ig)$ be the smallest positive eigenv…
Strongly localized semiclassical states for nonlinear Dirac equations
Thomas Bartsch, Tian Xu
We study semiclassical states of the nonlinear Dirac equation \[ -i\hbar\partial_tψ= ic\hbar\sum_{k=1}^3α_k\partial_kψ- mc^2βψ- M(x)ψ+ f(|ψ|)ψ,\quad t\in\mathbb{R},\ x\in\mathbb{R}…
A variational analysis of the spinorial Yamabe equation on product manifolds
Yannick Sire, Tian Xu
This work is devoted to the analysis of the Yamabe problem on Spin manifolds and some applications to CMC immersions. Despite the efforts of many authors, very little is known on t…
Blow-up profile for spinorial Yamabe type equation on
Tian Xu
Motivated by recent progress on a spinorial analogue of the Yamabe problem in the geometric literature, we study a conformally invariant spinor field equation on the -sphere, $m…
A spinorial analogue of the Brezis-Nirenberg theorem involving the critical Sobolev exponent
Thomas Bartsch, Tian Xu
Let be a compact Riemannian spin manifold of dimension , let denote the spinor bundle on , and let be the Atiyah-Singer Dirac oper…
Conformal embeddings of with prescribed mean curvature: A variational approach
Tian Xu
Motivated by recent progress on a spinorial analogue of the Yamabe problem in the geometric literature, we study a conformally invariant spinor field equation on the -sphere, $m…
Localized concentration of semi-classical states for nonlinear Dirac equations
Yanheng Ding, Tian Xu
The present paper studies concentration phenomena of semiclassical approximation of a massive Dirac equation with general nonlinear self-coupling: \[ -i\hbarα\cdot\nabla w+aβw+V(x)…
On the concentration of semi-classical states for a nonlinear Dirac-Klein-Gordon system
Yanheng Ding, Tian Xu
In the present paper, we study the semi-classical approximation of a Yukawa-coupled massive Dirac-Klein-Gordon system with some general nonlinear self-coupling. We prove that for a…