Simons' equation and minimal hypersurfaces in space forms
Biao Wang
TL;DR
This paper characterizes complete minimal hypersurfaces in space forms that satisfy Simons' equation, showing that only catenoids and Clifford minimal hypersurfaces meet this criterion.
Contribution
It proves a uniqueness result for minimal hypersurfaces satisfying Simons' equation in space forms, identifying specific known examples as the only solutions.
Findings
Catenoids satisfy Simons' equation in space forms.
Clifford minimal hypersurfaces satisfy Simons' equation.
These are the only complete minimal hypersurfaces with this property.
Abstract
In this paper, we show that the catenoids and the Clifford minimal hypersurfaces are the only complete minimal hypersurfaces satisfying the Simons' equation (3.9) in the space forms.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Algebraic and Geometric Analysis