Symmetries of geometric flows

By applying the theory of group-invariant solutions we investigate the symmetries of Ricci flow and hyperbolic geometric flow both on Riemann surfaces. The warped products on $\mathcal {S}^{n+1}$ of both flows are also studied.Comment: 27 page

Horava-Lifshitz Type Quantum Field Theory and Hierarchy Problem

We study the Lifshitz type extension of the standard model (SM) at UV, with dynamical critical exponent z=3. One loop radiative corrections to the Higgs mass in such a model is calculated. Our result shows that, the Hierarchy problem, which has initiated many excellent extension of the minimal SM, can be weakened in the z=3 Lifshitz type quantum field theory.Comment: 8 pages, 2 figure