高斯曲率的离散格式及其收敛性
Discrete schemes for Gaussian curvature and their convergence
AI总结：
本文综述了高斯曲率的几种离散格式，提出了一种新的离散格式并证明了其在价数不小于5的正则顶点处的收敛性，同时通过反例表明价数为4时无法构造收敛的离散格式，最后比较了多种离散格式的渐近误差。
摘要：
本文综述了高斯曲率的几种离散格式。考虑了一种修正的高斯曲率离散格式的收敛性。此外，提出了一种新的高斯曲率离散格式。我们证明了新格式在价数不小于5的正则顶点处收敛。通过构造反例，我们还表明不可能构建一个在价数为4的正则顶点处收敛的高斯曲率离散格式。最后，比较了几种高斯曲率离散格式的渐近误差。
英文摘要：
In this paper, several discrete schemes for Gaussian curvature are surveyed. The convergence property of a modified discrete scheme for the Gaussian curvature is considered. Furthermore, a new discrete scheme for Gaussian curvature is resented. We prove that the new scheme converges at the regular vertex with valence not less than 5. By constructing a counterexample, we also show that it is impossible for building a discrete scheme for Gaussian curvature which converges over the regular vertex with valence 4. Finally, asymptotic errors of several discrete scheme for Gaussian curvature are compared.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
