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<p>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 <i>N</i> and curvature <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10473_2025_116_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\frac 1 N\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> </math></EquationSource> </InlineEquation>.</p>

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On the Gaussian kinematic formula of R. Adler and J. Taylor

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • Joseph H. G. Fu

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 \(\frac 1 N\) 1 N .