函数k(u)=▏sinu▏+a所确定的Wulff形
Wulff Shape Determined by the Function k(u)=▏sinu▏+a
DOI: 10.12677/AAM.2023.125217, PDF,   
作者: 周小静, 蓝一涵：贵州师范大学数学科学学院，贵州 贵阳
关键词: 支持函数；正连续函数；Wulff形；Support Function； Positive Continuous Function； Wulff Shape
摘要: 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。
Abstract: 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.
文章引用：周小静, 蓝一涵. 函数k(u)=▏sinu▏+a所确定的Wulff形[J]. 应用数学进展, 2023, 12(5): 2138-2142. https://doi.org/10.12677/AAM.2023.125217

参考文献

[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] Böröczky, K.J., Lutwak, E., Yang, D. and Zhang, G.Y. (2012) The Log-Brunn-Minkowski Inequality. Advances in Mathematics, 231, 1974-1997. [Google Scholar] [CrossRef] 
[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. [Google Scholar] [CrossRef] 
[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. [Google Scholar] [CrossRef] 
[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. [Google Scholar] [CrossRef] 

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