|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'500'096
Articles rated: 2609
19 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Around the A.D. Alexandrov's theorem on a characterization of a sphere | | Victor Alexandrov
; | | Date: |
20 Dec 2012 | | Abstract: | This is a survey paper on various results relates to the following theorem
first proved by A.D. Alexandrov: extit{Let $S$ be an analytic convex
sphere-homeomorphic surface in $mathbb R^3$ and let
$k_1(oldsymbol{x})leqslant k_2(oldsymbol{x})$ be its principal curvatures
at the point $oldsymbol{x}$. If the inequalities
$k_1(oldsymbol{x})leqslant kleqslant k_2(oldsymbol{x})$ hold true with
some constant $k$ for all $oldsymbol{x}in S$ then $S$ is a sphere.} The
imphases is on a result of Y. Martinez-Maure who first proved that the above
statement is not valid for convex $C^2$-surfaces. For convenience of the
reader, in addendum we give a Russian translation of that paper by Y.
Martinez-Maure originally published in French in extit{C. R. Acad. Sci.,
Paris, S’{e}r. I, Math.} {f 332} (2001), 41--44. | | Source: | arXiv, 1212.5047 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER