A general geometric construction for affine surface area

Details A general geometric construction for affine surface area A general geometric construction for affine surface area

1997-06-30

arxiv.org/abs/math/9706215v1

Mathematics

Metric Geometry

Scientific paper

Let $K$ be a convex body in ${\bf R}^n$ and $B$ be the Euclidean unit ball in ${\bf R}^n$. We show that $$\mbox{lim}_{t\rightarrow 0} \frac{|K| -|K_t|}{|B| - |B_t|}= \frac{as(K)}{as(B)},$$ where $as(K)$ respectively $as(B)$ is the affine surface area of $K$ respectively $B$ and $\{K_t\}_{t\geq 0}$, $\{B_t\}_{t\geq 0}$ are general families of convex bodies constructed from $K$, $B$ satifying certain conditions. As a corollary we get results obtained in [M-W], [Schm],[S-W] and[W].

Affiliated with

Also associated with

No associations

Rating

A general geometric construction for affine surface area does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A general geometric construction for affine surface area, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A general geometric construction for affine surface area will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-37575