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| 1 | Time-periodic solutions of the Einstein's field equations Ⅰ:general framework显示文摘In this paper,we develop a new algorithm to find the exact solutions of the Einstein's field equations.Time-periodic solutions are constructed by using the new algorithm.The singularities of the time-periodic solutions are investigated and some new physical phenomena,such as degenerate event horizon and time-periodic event horizon,are found.The applications of these solutions in modern cosmology and general relativity are expected. | KONG DeXing1 & LIU KeFeng2 1Department of Mathematics,Zhejiang University,Hangzhou 310027,China 2Department of Mathematics,University of California at Los Angeles,CA 90095,USA | 2010 | Science China Mathematics2010，53，5： | 5 |
| 2 | Symmetries and solutions to geometrical flows显示文摘In this paper,we investigate group-invariant solutions to the hyperbolic geometric flow on Riemann surfaces,which include solutions of separation variables,traveling wave solutions,self-similar solutions and radial solutions.In the proceeding of reduction,there are elliptic,hyperbolic and mixed types of equations.For the first kind of equation,some exact solutions are found;while for the last two kinds,with implicit solutions found,we furthermore investigate whether there will be a global solution or blowing up.Referring to the work of Kong et al.(2009),the results come out perfectly. | WANG JinHua | 2013 | Science China Mathematics2013，56，8： | 3 |
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