论文标题
双曲线空间中的非均匀膨胀流
Nonhomogeneous expanding flows in hyperbolic spaces
论文作者
论文摘要
最近的一篇论文[CGT]研究了欧几里得空间的星形平均凸出突出的演变，这是通过一类非均匀扩展的曲率流的演变。在本文中，我们考虑了在真实，复杂和Quaternion的双曲线空间中存在相同的问题，研究了环境空间的较丰富几何形状如何影响进化。在每种情况下，都保留了初始条件，并证明了流量的长期存在。环境空间的几何形状会影响流动的渐近行为：在适当重新缩放诱导的度量标准后，如果环境歧管是真正的双曲线空间，则诱导的指标会收敛到标准的riemannian圆形公制的形式，否则它将其融合到标准的亚里曼尼亚式标准的奇数偏差的标准次数。最后，在每种情况下，我们都能够构造许多示例，以使极限没有恒定的标态曲率。
A recent paper [CGT] studies the evolution of star-shaped mean convex hypersurfaces of the Euclidean space by a class of nonhomogeneous expanding curvature flows. In the present paper we consider the same problem in the real, complex and quaternionic hyperbolic spaces, investigating how the richer geometry of the ambient space affects the evolution. In every case the initial conditions are preserved and the long time existence of the flow is proven. The geometry of the ambient space influences the asymptotic behaviour of the flow: after a suitable rescaling the induced metric converges to a conformal multiple of the standard Riemannian round metric of the sphere if the ambient manifold is the real hyperbolic space, otherwise it converges to a conformal multiple of the standard sub-Riemannian metric on the odd-dimensional sphere. Finally, in every cases, we are able to construct infinitely many examples such that the limit does not have constant scalar curvature.
