Constructions of $$H_r$$ H r -hypersurfaces, barriers and Alexandrov theorem in $$\mathrm{I\!H}^n\times \mathrm{I\!R}$$ I H n × I R

Verfasser / Beitragende:
[Maria Elbert, Ricardo Sa Earp]
Ort, Verlag, Jahr:
2015
Enthalten in:
Annali di Matematica Pura ed Applicata (1923 -), 194/6(2015-12-01), 1809-1834
Format:
Artikel (online)
Online Zugang:
Get it Online (National Licence)
ID: 605496102
LEADER caa a22 4500
001 605496102
003 CHVBK
005 20210128100534.0
007 cr unu---uuuuu
008 210128e20151201xx s 000 0 eng
024 7 0 |a 10.1007/s10231-014-0446-y  |2 doi 
035 |a (NATIONALLICENCE)springer-10.1007/s10231-014-0446-y 
245 0 0 |a Constructions of $$H_r$$ H r -hypersurfaces, barriers and Alexandrov theorem in $$\mathrm{I\!H}^n\times \mathrm{I\!R}$$ I H n × I R  |h [Elektronische Daten]  |c [Maria Elbert, Ricardo Sa Earp] 
520 3 |a In this paper, we are concerned with hypersurfaces in $$\mathrm{I\!H}\times \mathrm{I\!R}$$ I H × I R with constant $$r$$ r -mean curvature, to be called $$H_r$$ H r -hypersurfaces. We construct examples of complete $$H_r$$ H r -hypersurfaces, which are invariant by parabolic screw motion or by rotation. We prove that there is a unique rotational strictly convex entire $$H_r$$ H r -graph for each value $$0\frac{n-r}{n}$$ H r > n - r n , there is a unique embedded compact strictly convex rotational $$H_r$$ H r -hypersurface. By using them as barriers, we obtain some interesting geometric results, including height estimates and an Alexandrov-type Theorem. Namely, we prove that an embedded compact $$H_r$$ H r -hypersurface in $$\mathrm{I\!H}^n\times \mathrm{I\!R}$$ I H n × I R is rotational ( $$H_r>0$$ H r > 0 ). 
540 |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 
690 7 |a $$r$$ r -Mean curvature  |2 nationallicence 
690 7 |a Alexandrov Theorem  |2 nationallicence 
690 7 |a $$H_r$$ H r -Hypersurfaces  |2 nationallicence 
690 7 |a Barriers  |2 nationallicence 
690 7 |a Entire vertical graphs  |2 nationallicence 
690 7 |a Complete horizontal graphs  |2 nationallicence 
700 1 |a Elbert  |D Maria  |u Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil  |4 aut 
700 1 |a Sa Earp  |D Ricardo  |u Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Brazil  |4 aut 
773 0 |t Annali di Matematica Pura ed Applicata (1923 -)  |d Springer Berlin Heidelberg  |g 194/6(2015-12-01), 1809-1834  |x 0373-3114  |q 194:6<1809  |1 2015  |2 194  |o 10231 
856 4 0 |u https://doi.org/10.1007/s10231-014-0446-y  |q text/html  |z Onlinezugriff via DOI 
898 |a BK010053  |b XK010053  |c XK010000 
900 7 |a Metadata rights reserved  |b Springer special CC-BY-NC licence  |2 nationallicence 
908 |D 1  |a research-article  |2 jats 
949 |B NATIONALLICENCE  |F NATIONALLICENCE  |b NL-springer 
950 |B NATIONALLICENCE  |P 856  |E 40  |u https://doi.org/10.1007/s10231-014-0446-y  |q text/html  |z Onlinezugriff via DOI 
950 |B NATIONALLICENCE  |P 700  |E 1-  |a Elbert  |D Maria  |u Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil  |4 aut 
950 |B NATIONALLICENCE  |P 700  |E 1-  |a Sa Earp  |D Ricardo  |u Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Brazil  |4 aut 
950 |B NATIONALLICENCE  |P 773  |E 0-  |t Annali di Matematica Pura ed Applicata (1923 -)  |d Springer Berlin Heidelberg  |g 194/6(2015-12-01), 1809-1834  |x 0373-3114  |q 194:6<1809  |1 2015  |2 194  |o 10231 

Verknüpfte Einträge