The Teichmüller harmonic map flow, introduced by Rupflin and Topping (2012) [11], evolves both a map from a closed Riemann surface to an arbitrary compact Riemannian manifold, and a constant curvature metric on the domain, in order to reduce its harmonic map energy as quickly as possible. In this paper, we develop the geometric analysis of holomorphic quadratic differentials in order to explain what happens in the case that the domain metric of the flow degenerates at infinite time. We obtain a branched minimal immersion from the degenerate domain. 相似文献
Based on the extended Huygens–Fresnel principle and the unified theory of coherence and polarization of light, we investigate the propagation properties of a radially polarized beam through turbulent ocean. Analytic formulae for the spectral density, the spectral degree of polarization, and the beam characteristics of such a beam on propagation are discussed. It is shown that under the influence of oceanic turbulence, the radially polarized beam will change to a partially polarized one and the beam profile will approach to a Gaussian distribution. 相似文献
For a sequence of approximate Dirac-harmonic maps from a closed spin Riemann surface into a stationary Lorentzian manifold with uniformly bounded energy, we study the blow-up analysis and show that the Lorentzian energy identity holds. Moreover, when the targets are static Lorentzian manifolds, we prove the positive energy identity and the no neck property.
The modernization and marketing of traditional Chinese medicine is difficult primarily because its pharmacodynamic material basis has not been elucidated. Moreover, a central problem is the lack of effective research methods and strategies. After >20 years of study, here, we propose the theory of pharmacodynamic differential serum chromatography. The method described here can be used to identify (and possibly develop) effective pharmacodynamic materials. In light of the theory, we identified hydroxysafflor yellow A (HSYA) to be the effective pharmacodynamic material of Carthamus tinctorius L. (safflower). With the help of the methodology described here, the modernization and understanding of traditional Chinese medicine may be accelerated.