Volume 15, Issue 3
Starshaped Compact Hypersurfaces with Prescribed M-th Mean Curvature in Elliptic Space

Yanyan Li & I. Oliker Vladimir

J. Part. Diff. Eq., 15 (2002), pp. 68-80.

Published online: 2002-08

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  • Abstract
We consider the problem of finding a compact starshaped hypresurface in a space form for which the normalized m-th elementary symmetric function of principal curvatures is a prescribed function. In this paper the conditions for the existence of at least one solution to a nonlinear second order elliptic equation of that problem are established in case of a space form with positive sectional curvature.
  • Keywords

Nonlinear elliptic equations Spaces of constant sectional curvature Hypersurfaces with prescribed curvature functions

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@Article{JPDE-15-68, author = {}, title = {Starshaped Compact Hypersurfaces with Prescribed M-th Mean Curvature in Elliptic Space}, journal = {Journal of Partial Differential Equations}, year = {2002}, volume = {15}, number = {3}, pages = {68--80}, abstract = { We consider the problem of finding a compact starshaped hypresurface in a space form for which the normalized m-th elementary symmetric function of principal curvatures is a prescribed function. In this paper the conditions for the existence of at least one solution to a nonlinear second order elliptic equation of that problem are established in case of a space form with positive sectional curvature.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5456.html} }
TY - JOUR T1 - Starshaped Compact Hypersurfaces with Prescribed M-th Mean Curvature in Elliptic Space JO - Journal of Partial Differential Equations VL - 3 SP - 68 EP - 80 PY - 2002 DA - 2002/08 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5456.html KW - Nonlinear elliptic equations KW - Spaces of constant sectional curvature KW - Hypersurfaces with prescribed curvature functions AB - We consider the problem of finding a compact starshaped hypresurface in a space form for which the normalized m-th elementary symmetric function of principal curvatures is a prescribed function. In this paper the conditions for the existence of at least one solution to a nonlinear second order elliptic equation of that problem are established in case of a space form with positive sectional curvature.
Yanyan Li & I. Oliker Vladimir . (2019). Starshaped Compact Hypersurfaces with Prescribed M-th Mean Curvature in Elliptic Space. Journal of Partial Differential Equations. 15 (3). 68-80. doi:
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