Simons type formulas for surfaces in Sol_3 and applications
Dorel Fetcu
TL;DR
This paper derives Simons type formulas for surfaces in Sol_3, enabling new gap results for compact constant mean curvature surfaces by analyzing the Laplacian of the second fundamental form.
Contribution
It introduces a novel Simons type formula specific to surfaces in Sol_3, facilitating the study of geometric properties of constant mean curvature surfaces in this space.
Findings
Derived the Laplacian of the squared norm of the second fundamental form in Sol_3.
Obtained gap results for compact constant mean curvature surfaces.
Provided new insights into the geometry of surfaces in Sol_3.
Abstract
We compute the Laplacian of the squared norm of the second fundamental form of a surface in Sol_3 and then use this Simons type formula to obtain some gap results for compact constant mean curvature surfaces of this space.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Nonlinear Partial Differential Equations