Translating solitons of mean curvature flow of noncompact spacelike hypersurfaces in Minkowski space

In this paper, we study the existence, uniqueness and asymptotic behavior of rotationally symmetric translating solitons of the mean curvature flow in Minkowski space. We also study the asymptotic behavior and the strict convexity of general solitons of such flows.Comment: 16page

Neutrino flavor instabilities in a time-dependent supernova model

A dense neutrino medium such as that inside a core-collapse supernova can experience collective flavor conversion or oscillations because of the neutral-current weak interaction among the neutrinos. This phenomenon has been studied in a restricted, stationary supernova model which possesses the (spatial) spherical symmetry about the center of the supernova and the (directional) axial symmetry around the radial direction. Recently it has been shown that these spatial and directional symmetries can be broken spontaneously by collective neutrino oscillations. In this paper we analyze the neutrino flavor instabilities in a time-dependent supernova model. Our results show that collective neutrino oscillations start at approximately the same radius in both the stationary and time-dependent supernova models unless there exist very rapid variations in local physical conditions on timescales of a few microseconds or shorter. Our results also suggest that collective neutrino oscillations can vary rapidly with time in the regimes where they do occur which need to be studied in time-dependent supernova models.Comment: 5 pages, 2 figures, version to appear in PL

Flavor instabilities in the neutrino line model

A dense neutrino medium can experience collective flavor oscillations through nonlinear neutrino-neutrino refraction. To make this multi-dimensional flavor transport problem more tractable, all existing studies have assumed certain symmetries (e.g., the spatial homogeneity and directional isotropy in the early universe) to reduce the dimensionality of the problem. In this work we show that, if both the directional and spatial symmetries are not enforced in the neutrino line model, collective oscillations can develop in the physical regimes where the symmetry-preserving oscillation modes are stable. Our results suggest that collective neutrino oscillations in real astrophysical environments (such as core-collapse supernovae and black-hole accretion discs) can be qualitatively different from the predictions based on existing models in which spatial and directional symmetries are artificially imposed.Comment: 5 pages, 1 figur