caa a22 4500 60549598X CHVBK 20210128100534.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10231-013-0367-1 doi (NATIONALLICENCE)springer-10.1007/s10231-013-0367-1 Curvature estimates for properly immersed $$\phi _{h}$$ ϕ h -bounded submanifolds [Elektronische Daten] [G. Bessa, Barnabe Lima, Leandro Pessoa] Jorge-Koutrofiotis (Am J Math 103:711-725, 1980) and Pigola et al. (Memoirs Am Math Soc 174(822), 2005) proved sharp sectional curvature estimates for extrinsically bounded submanifolds. In Alías et al. (Trans Am Math Soc 364(7):3513-3528, 2012), Alias et al. showed that these estimates hold on properly immersed cylindrically bounded submanifolds. On the other hand, Alias et al. (Math Ann 345(2):367-376, 2009) proved mean curvature estimates for properly immersed cylindrically bounded submanifolds. In this paper, we prove these sectional and mean curvature estimates for a larger class of submanifolds, the properly immersed $$\phi $$ ϕ -bounded submanifolds, see Theorems5 and 6. With the ideas developed, we prove stronger forms of these estimates, see the results in Sect.4. Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2013 Curvature estimates nationallicence $$\phi $$ ϕ -Bounded submanifolds nationallicence Omori-Yau pairs nationallicence Omori-Yau maximum principle nationallicence Bessa G. Department of Mathematics, Universidade Federal do Ceará-UFC, 60455-760, Fortaleza, CE, Brazil aut Lima Barnabe Department of Mathematics, Universidade Federal do Piauí-UFPI, 64049-550, Teresina, PI, Brazil aut Pessoa Leandro Department of Mathematics, Universidade Federal do Piauí-UFPI, 64049-550, Teresina, PI, Brazil aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/1(2015-02-01), 109-130 0373-3114 194:1<109 2015 194 10231 https://doi.org/10.1007/s10231-013-0367-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-013-0367-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bessa G. Department of Mathematics, Universidade Federal do Ceará-UFC, 60455-760, Fortaleza, CE, Brazil aut NATIONALLICENCE 700 1- Lima Barnabe Department of Mathematics, Universidade Federal do Piauí-UFPI, 64049-550, Teresina, PI, Brazil aut NATIONALLICENCE 700 1- Pessoa Leandro Department of Mathematics, Universidade Federal do Piauí-UFPI, 64049-550, Teresina, PI, Brazil aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/1(2015-02-01), 109-130 0373-3114 194:1<109 2015 194 10231