Surfaces and Hypersurfaces with Prescribed Radial Mean Curvature

Marcelo Lopes Ferro; Armando M. V. Corro

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arXiv · 2510.11669

Surfaces and Hypersurfaces with Prescribed Radial Mean Curvature

Marcelo Lopes Ferro·Armando M. V. Corro

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Abstract

In this work, we provide a local classification of certain special classes of surfaces determined by the prescription of the radial mean curvature in terms of the height and angle functions. Moreover, we introduce a special class of hypersurfaces, and we also provide a local classification of these three-dimensional hypersurfaces whose second mean curvature vanishes. Finally, we present a recursive method for constructing such hypersurfaces, extending the same curvature prescription approach to higher dimensions.

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Marcelo Lopes Ferro, Armando M. V. Corro. 2025-10-13. Surfaces and Hypersurfaces with Prescribed Radial Mean Curvature. https://arxiv.org/abs/2510.11669

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