|
函数k(u)=▏sinu▏+a所确定的Wulff形
|
Abstract:
凸体是积分几何和凸几何分析的重要内容,Wulff形作为一类特殊凸体,具有一定研究价值。利用凸体的支持函数与函数性质,研究函数k(u)=▏sinu▏+a所确定的Wulff形,给出Wulff形的周长和面积的计算公式。
Convex body is an important part of integral geometry and convex geometry analysis. As a special convex body, Wulff shape has certain research value. By using the support functions of convex bod-ies and function properties, this paper discusses the Wulff shape determined by the function k(u)=▏sinu▏+a , given the formula for calculating the perimeter and area of the Wulff shape.
[1] | 任德麟. 积分几何引论[M]. 上海: 上海科学技术出版社, 1998. |
[2] | 梅向明, 黄敬之. 微分几何[M]. 北京: 高等教育出版社, 2019. |
[3] | B?r?czky, K.J., Lutwak, E., Yang, D. and Zhang, G.Y. (2012) The Log-Brunn-Minkowski Inequality. Advances in Mathematics, 231, 1974-1997. https://doi.org/10.1016/j.aim.2012.07.015 |
[4] | He, Y.J. and Li, H.Z. (2008) Integral Formula of Minkowski Type and New Characterization of the Wulff Shape. Acta Mathematica Sinica (English Series), 24, 697-704. https://doi.org/10.1007/s10114-007-7116-6 |
[5] | Li, A.J., Huang, Q.Z. and Xi, D.M. (2017) Volume Inequalities for Sections and Projections of Wulff Shapes and Their Polars. Advances in Applied Mathematics, 91, 76-97. https://doi.org/10.1016/j.aam.2017.05.010 |
[6] | Han, H.H. and Nishimura, T. (2017) Strictly Convex Wulff Shapes and C1 Convex Integrands. Proceedings of the American Mathematical Society, 145, 3997-4008. https://doi.org/10.1090/proc/13510 |