黃彥彰 教授 ( 國立台南大學應用數學系 )

演講時間：113年3月5日下午1點30分
演講地點：A813

講題：A surface area formula for compact hypersurfaces in the Euclidean spaces

摘要：The classical Cauchy surface area formula, a cornerstone in geometry,
offers a method for computing the surface area of convex bodies in n-dimensional Euclidean space by averaging their projected areas over the unit sphere.

In this presentation, we employ Lie group theory to introduce a fresh perspective onprojected area onto subspaces,

thus expanding Cauchy's formula to non-convex domains.

Notably, this extension concurs with De Jong's formula derived through tubular neighborhoods,

while our approach provides a concise proof for Crofton's formula.

Moreover, we define projected volumes of higher codimension (referred to as projected r-volumes, where r ≤ n)

onto r-dimensional subspaces and establish a recursive formula for their mean projected values.