{"title":"Classes of Noncontact Mappings of Carnot Groups and Metric Properties","authors":"M. B. Karmanova","doi":"10.1134/s0037446623060083","DOIUrl":null,"url":null,"abstract":"<p>We study the metric properties of level surfaces\nfor classes of smooth noncontact mappings\nfrom arbitrary Carnot groups into two-step ones\nwith some constraints on the dimensions of horizontal subbundles\nand the subbundles corresponding to degree 2 fields.\nWe calculate the Hausdorff dimension of the level surfaces\nwith respect to the sub-Riemannian quasimetric\nand derive an analytical relation between the Hausdorff measures\nfor the sub-Riemannian quasimetric and the Riemannian metric.\nAs application,\nwe establish a new form of coarea formula, also proving that\nthe new coarea factor is well defined.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0037446623060083","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We study the metric properties of level surfaces
for classes of smooth noncontact mappings
from arbitrary Carnot groups into two-step ones
with some constraints on the dimensions of horizontal subbundles
and the subbundles corresponding to degree 2 fields.
We calculate the Hausdorff dimension of the level surfaces
with respect to the sub-Riemannian quasimetric
and derive an analytical relation between the Hausdorff measures
for the sub-Riemannian quasimetric and the Riemannian metric.
As application,
we establish a new form of coarea formula, also proving that
the new coarea factor is well defined.