Curvature estimates for submanifolds with prescribed Gauss image and mean curvature

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dc.creatorXin, Y. L.
dc.date2008-12-19
dc.date.accessioned2026-07-07T12:20:49Z
dc.date.available2026-07-07T12:20:49Z
dc.descriptionWe study that the $n-$graphs defining by smooth map $f:\Om\subset \ir{n}\to \ir{m}, m\ge 2,$ in $\ir{m+n}$ of the prescribed mean curvature and the Gauss image. We derive the interior curvature estimates $$\sup_{D_R(x)}|B|^2\le\f{C}{R^2}$$ under the dimension limitations and the Gauss image restrictions. If there is no dimension limitation we obtain $$\sup_{D_R(x)}|B|^2\le C R^{-a}\sup_{D_{2R}(x)}(2-\De_f)^{-(\f{3}{2}+\f{1}{s})}, \qquad s=\min(m, n)$$ with $a<1$ under the condition $$\De_f=[\text{det}(\de_{ij}+\sum_\a\pd{f^\a}{x^i}\pd{f^\a}{x^j})]^{\f{1}{2}}<2.$$ If the image under the Gauss map is contained in a geodesic ball of the radius $\f{\sqrt{2}}{4}π$ in $\grs{n}{m}$ we also derive corresponding estimates.
dc.identifierhttps://arxiv.org/abs/0812.3710
dc.identifierhttp://arxiv.org/abs/0812.3710
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/213179
dc.subjectDifferential Geometry
dc.subject49Q05, 53A07, 53A10
dc.titleCurvature estimates for submanifolds with prescribed Gauss image and mean curvature
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