A note on surfaces with parallel mean curvature
Dorel Fetcu, Harold Rosenberg
TL;DR
This paper characterizes complete non-minimal surfaces with parallel mean curvature and non-negative Gaussian curvature using a Simons type equation, providing insights into their geometric properties.
Contribution
It introduces a novel application of a Simons type equation to classify pmc surfaces with specific curvature conditions.
Findings
Characterization of pmc surfaces with non-negative Gaussian curvature
Identification of geometric properties using Simons type equation
Advancement in understanding complete non-minimal pmc surfaces
Abstract
We use a Simons type equation in order to characterize complete non-minimal pmc surfaces with non-negative Gaussian curvature.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Nonlinear Partial Differential Equations