ON THE GAUSSIAN KINEMATIC FORMULA OF R. ADLER AND J. TAYLOR

ON THE GAUSSIAN KINEMATIC FORMULA OF R. ADLER AND J. TAYLOR

ON THE GAUSSIAN KINEMATIC FORMULA OF R. ADLER AND J. TAYLOR

ON THE GAUSSIAN KINEMATIC FORMULA OF R. ADLER AND J. TAYLOR

ON THE GAUSSIAN KINEMATIC FORMULA OF R. ADLER AND J. TAYLOR

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doi:10.1007/s10473-025-0116-8

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (1): 200-214.doi: 10.1007/s10473-025-0116-8

Joseph H.G. Fu

Department of Mathematics, University of Georgia, Athens, GA 30602, USA

收稿日期:2024-09-04 发布日期:2025-02-06
作者简介:Joseph H.G. Fu, E-mail,: joefu@uga.edu

Joseph H.G. Fu

Department of Mathematics, University of Georgia, Athens, GA 30602, USA

Received:2024-09-04 Published:2025-02-06
About author:Joseph H.G. Fu, E-mail,: joefu@uga.edu

摘要： We apply methods of algebraic integral geometry to prove a special case of the Gaussian kinematic formula of Adler-Taylor. The idea, suggested already by Adler and Taylor, is to view the GKF as the limit of spherical kinematic formulas for spheres of large dimension $N$ and curvature $\frac 1 N$ .

关键词: integral geometry, kinematic formula, probability density, Gaussian density

Abstract: We apply methods of algebraic integral geometry to prove a special case of the Gaussian kinematic formula of Adler-Taylor. The idea, suggested already by Adler and Taylor, is to view the GKF as the limit of spherical kinematic formulas for spheres of large dimension $N$ and curvature $\frac 1 N$ .

Key words: integral geometry, kinematic formula, probability density, Gaussian density

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52A22

Joseph H.G. Fu. ON THE GAUSSIAN KINEMATIC FORMULA OF R. ADLER AND J. TAYLOR[J]. 数学物理学报(英文版), 2025, 45(1): 200-214.

Joseph H.G. Fu. ON THE GAUSSIAN KINEMATIC FORMULA OF R. ADLER AND J. TAYLOR[J]. Acta mathematica scientia,Series B, 2025, 45(1): 200-214.

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