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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Forthcoming papers   > Article

[FORTHCOMING] The class of second fundamental forms arising from minimal immersions in a space form

[FORTHCOMING] La classe des secondes formes fondamentales résultant d’immersions minimales dans un espace forme


Marcello Lucia
The City University of New York
USA



Validated on 5 February 2024   DOI : TBA

Abstract

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The second fundamental form arising from an oriented minimal immersion of a closed surface in a space form satisfies several constraints. One of them is provided by the Gauss-Codazzi equation that can be rephrased as a semilinear problem on the surface. We discuss some results for these type of nonlinear problems and analyze the behaviors of the solutions when the hyperbolic norm of the second fundamental form is small.

The second fundamental form arising from an oriented minimal immersion of a closed surface in a space form satisfies several constraints. One of them is provided by the Gauss-Codazzi equation that can be rephrased as a semilinear problem on the surface. We discuss some results for these type of nonlinear problems and analyze the behaviors of the solutions when the hyperbolic norm of the second fundamental form is small.

space forms minimal surfaces semilinear elliptic equations variational methods blowup analysis

space forms minimal surfaces semilinear elliptic equations variational methods blowup analysis