E-resources
Peer reviewed
Open access
-
Yen-Chang Huang
Journal of inequalities and applications, 04/2024, Volume: 2024, Issue: 1Journal Article
Abstract The classical Cauchy surface area formula states that the surface area of the boundary ∂ K = Σ $\partial K=\Sigma $ of any n-dimensional convex body in the n-dimensional Euclidean space R n $\mathbb{R}^{n}$ can be obtained by the average of the projected areas of Σ along all directions in S n − 1 $\mathbb{S}^{n-1}$ . In this note, we generalize the formula to the boundary of arbitrary n-dimensional submanifold in R n $\mathbb{R}^{n}$ by introducing a natural notion of projected areas along any direction in S n − 1 $\mathbb{S}^{n-1}$ . This surface area formula derived from the new notion coincides with not only the result of the Crofton formula but also with that of De Jong (Math. Semesterber. 60(1):81–83, 2013) by using a tubular neighborhood. We also define the projected r-volumes of Σ onto any r-dimensional subspaces and obtain a recursive formula for mean projected r-volumes of Σ.
Author
![loading ... loading ...](themes/default/img/ajax-loading.gif)
Shelf entry
Permalink
- URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year | Impact factor | Edition | Category | Classification | ||||
---|---|---|---|---|---|---|---|---|
JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
Select the library membership card:
If the library membership card is not in the list,
add a new one.
DRS, in which the journal is indexed
Database name | Field | Year |
---|
Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
---|
Source: Personal bibliographies
and: SICRIS
The material is available in full text. If you wish to order the material anyway, click the Continue button.