A rigidity theorem for ideal surfaces with flat boundary (Q2291462)
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scientific article; zbMATH DE number 7240878
- A Rigidity Theorem for Ideal Surfaces with Flat Boundary
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A rigidity theorem for ideal surfaces with flat boundary |
scientific article; zbMATH DE number 7240878 |
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A rigidity theorem for ideal surfaces with flat boundary (English)
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A Rigidity Theorem for Ideal Surfaces with Flat Boundary (English)
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31 January 2020
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27 August 2020
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The authors show that a surface \(\Sigma\) embedded in \(\mathbb R^3\) satisfying a certain sixth-order nonlinear PDE must be a part of a flat plane. Such a condition is related with the optimization of the \(L^2\)-norm of the gradient of the mean curvature. The proof is achieved by combining several inequalities on the properties of the curvature of the solutions to the PDE.
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sixth-order elliptic equation
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Neumann boundary condition
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second fundamental form
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energy
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normal variation
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boundary value
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0.9890405535697936
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0.7373942136764526
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0.7353898882865906
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