欧氏空间点态凸性模的表示

 讨论了点态凸性模在二维和三维欧氏空间的表示，并给出其在曲面为椭圆和椭球面的特殊点处的计算。通过计算可以看出其点态凸性模的值在长轴最小，沿曲面从长轴到短轴点态凸性模的值是递增的，达到短轴时最大，从而进一步说明椭圆的对称性，同时也说明点态凸性模的值越小，该点的凸性程度越强。

Representations of Pointwise Convex Modulus in Euclidean Spaces

With a support function as a tool, the estimations and representations of pointwise convex modulus in two-dimensional and three-dimensional Euclidean spaces are discussed, and the calculations of the pointwise convex modulus in the surface of ellipse and ellipsoid surface are carried out. It is shown that the smaller this spot, the stronger its convexity degree. The convex modulus describes an overall degree of convexity of the unit sphere in the space, which is very different from the degree of convexity at each point and which may have very great influence on the whole feature of the space. Therefore, the study of pointwise properties is very important. The pointwise constant geometry of the space can enhance the understanding of the nature of the space.