摘要
首先证明了凸函数的一个简单性质:次线性增长的单调增凸函数必然是常数,然后讨论了具有非负Ricci曲率的黎曼流形上热方程解的Boltzmann-Shannon熵,证明了它是单调增的凸函数,并由此给出古典解是常数的等价刻画,最后通过例子,说明了至少在非紧情形下,所给出的刻画是最优的.
This paper firstly demonstrates that any increasing convex function with sub-linear growth must bea constant by means of a simple property of convex functions. Then we study the Boltzmann-Shannonentropy of positive solutions to the heat equation on Riemannian manifolds with nonnegative Ricci curvature,and prove that this entropy belongs to a monotone ncreasing convex function, and thereout turns out thefundamental solutions to be an invariable equivalent characterization. In the end, it is illustrated via examplesthat such an invariable equivalent characterization is optimal at least under the noncompact manifoldsituation.
出处
《温州大学学报（自然科学版）》
2015年第1期6-10,共5页
Journal of Wenzhou University(Natural Science Edition)
基金
国家自然科学基金(11001203)
浙江省自然科学基金(LY13A010009)
