CAJ | 학술논문

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。
수선증명료철함수적일개간단성질：차선성증장적단조증철함수필연시상수，연후토론료구유비부Ricci곡솔적려만류형상열방정해적Boltzmann-Shannon적，증명료타시단조증적철함수，병유차급출고전해시상수적등개각화，최후통과례자，설명료지소재비긴정형하，소급출적각화시최우적。
This paper firstly demonstratesthatany increasing convex function with sub-linear growth must be a constant by means ofa simple property of convex functions.Then we study the Boltzmann-Shannon entropy of positive solutions to the heat equation on Riemannian manifolds with nonnegative Ricci curvature, and provethatthis entropybelongs toa monotonencreasing convex function,andthereoutturns out the fundamental solutions to be an invariable equivalentcharacterization.In the end, it is illustrated via examples that such an invariable equivalentcharacterization isoptimal at least underthenoncompact manifold situation.