A note on Sobolev isometric immersions below W-2,W-2 regularity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10370788" target="_blank" >RIV/00216208:11320/17:10370788 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.difgeo.2017.02.009" target="_blank" >http://dx.doi.org/10.1016/j.difgeo.2017.02.009</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.difgeo.2017.02.009" target="_blank" >10.1016/j.difgeo.2017.02.009</a>

Result language
angličtina
Original language name
A note on Sobolev isometric immersions below W-2,W-2 regularity
Original language description
This paper aims to investigate the Hessian of second order Sobolev isometric immersions below the natural W-2,W-2 setting. We show that the Hessian of each coordinate function of a W-2,W-p < 2, isometric immersion satisfies a low rank property in the almost everywhere sense, in particular, its Gaussian curvature vanishes almost everywhere. Meanwhile, we provide an example of a W-2,W-P, p < 2, isometric immersion from a bounded domain of R-2 into R-3 that has multiple singularities.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA15-08218S" target="_blank" >GA15-08218S: Theory of real functions and its applications in geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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