Bubbling analysis for approximate Lorentzian harmonic maps from Riemann surfaces (Q1688779)

This paper focusses on the study of harmonic maps from a Riemann surface \(M\) into a Lorentzian manifold \(N\times\mathbb{R}\) that is equipped with a warped product metric of the form \(g=g_N-\beta(d\theta+\omega)^2\), where \((N,g_N)\) is a compact Riemannian manifold, \((\mathbb{R},d\theta^2)\) is the 1-dimensional Euclidean space, \(\beta\) is a positive \(C^\infty\) function on \(N\) and \(\omega\) is a smooth 1-form on \(N\). In the main results of the article, the authors prove some energy identities of an approximate Lorentzian harmonic map sequence and get the no-neck property during a blow-up process, provided that \(M\) is a compact Riemann surface with boundary.