Morse inequalities for the area functional
Fernando C. Marques, Rafael Montezuma, Andr\'e Neves
TL;DR
This paper establishes strong Morse inequalities for the area functional in codimension one, providing new insights into the topology of minimal hypersurfaces within certain ambient dimensions.
Contribution
It proves the strong Morse inequalities for the area functional in codimension one for ambient dimensions between 3 and 7, in both closed and boundary cases.
Findings
Proved strong Morse inequalities for the area functional.
Applicable to ambient dimensions 3 to 7.
Addresses both closed and boundary cases.
Abstract
In this article we prove the strong Morse inequalities for the area functional in codimension one, assuming that the ambient dimension satisfies , in both the closed and the boundary cases.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Geometry and complex manifolds