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We give some optimal estimates of the height, curvature and volume of compact hypersurfaces in with constant curvature bounding a planar closed (n-1)-submanifold.
J. A. Gálvez, and A. Martínez. "Hypersurfaces with constant curvature in $ℝ^{n+1}$." Banach Center Publications 57.1 (2002): 101-108. <http://eudml.org/doc/281820>.
@article{J2002, abstract = {We give some optimal estimates of the height, curvature and volume of compact hypersurfaces in $ℝ^\{n+1\}$ with constant curvature bounding a planar closed (n-1)-submanifold.}, author = {J. A. Gálvez, A. Martínez}, journal = {Banach Center Publications}, keywords = {elliptic partial differential equations; Monge-Ampère type; height; curvature; compact hypersurfaces}, language = {eng}, number = {1}, pages = {101-108}, title = {Hypersurfaces with constant curvature in $ℝ^\{n+1\}$}, url = {http://eudml.org/doc/281820}, volume = {57}, year = {2002}, }
TY - JOUR AU - J. A. Gálvez AU - A. Martínez TI - Hypersurfaces with constant curvature in $ℝ^{n+1}$ JO - Banach Center Publications PY - 2002 VL - 57 IS - 1 SP - 101 EP - 108 AB - We give some optimal estimates of the height, curvature and volume of compact hypersurfaces in $ℝ^{n+1}$ with constant curvature bounding a planar closed (n-1)-submanifold. LA - eng KW - elliptic partial differential equations; Monge-Ampère type; height; curvature; compact hypersurfaces UR - http://eudml.org/doc/281820 ER -