In this paper, we define a new discrete curvature on two and three dimensional triangulated manifolds, which is a modification of the well-known discrete curvature on these manifolds. The new definition is more natural and respects the scaling exactly the same way as Gauss curvature does. Moreover, the new discrete curvature can be used to approximate the Gauss curvature on surfaces. Then we study the corresponding constant curvature problem, which is called the combinatorial Yamabe problem, by the corresponding combinatorial versions of Ricci flow and Calabi flow for surfaces and Yamabe flow for 3-dimensional manifolds. The basic tools are the discrete maximal principle and variational principle.

在本文中，我们在二维和三维三角歧管上定义了新的离散曲率，这是对这些歧管上众所周知的离散曲率的修改。新定义更加自然，并且与高斯曲率完全一样地遵循缩放。此外，新的离散曲率可用于近似表面上的高斯曲率。然后，我们通过表面的Ricci流和Calabi流以及3维流形的Yamabe流的对应组合形式研究相应的等曲率问题，称为组合Yamabe问题。基本工具是离散最大原理和变分原理。