E-resources
-
Chousionis, Vasilis; Magnani, Valentino; Tyson, Jeremy T.
Advances in mathematics (New York. 1965), 03/2020, Volume: 363Journal Article
We study uniform measures in the first Heisenberg group H equipped with the Korányi metric dH. We prove that 1-uniform measures are proportional to the spherical 1-Hausdorff measure restricted to an affine horizontal line, while 2-uniform measures are proportional to spherical 2-Hausdorff measure restricted to an affine vertical line. We also show that each 3-uniform measure which is supported on a vertically ruled surface is proportional to the restriction of spherical 3-Hausdorff measure to an affine vertical plane, and that no quadratic x3-graph can be the support of a 3-uniform measure. According to a result of Merlo, every 3-uniform measure is supported on a quadratic variety; in conjunction with our results, this shows that all 3-uniform measures are proportional to spherical 3-Hausdorff measure restricted to an affine vertical plane. We establish our conclusions by deriving asymptotic formulas for the measures of small extrinsic balls in (H,dH) intersected with smooth submanifolds. The coefficients in our power series expansions involve intrinsic notions of curvature associated to smooth curves and surfaces in H.
![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.