Shape stability of a quadrature surface problem in infinite Riemannian manifolds

Authors

Keywords:

Stability, quadrature surface, shape optimization, Riemannian manifold, Gauss- Bonnet theorem

Abstract

In this paper, we revisit a quadradure surface problem in shape optimization. With tools from infinite-dimensional Riemannian geometry, we give simple control over how an optimal shape can be characterized. The framework of the infinite-dimensional Riemannian manifold is essential in the control of optimal geometric shape. The covariant derivative plays a key role in calculating and analyzing the qualitative properties of the shape hessian. Control only depends on the mean curvature of the domain, which is a minimum or a critical point. In the two-dimensional case, Gauss-Bonnet's theorem gives a control within the framework of the algorithm for the minimum.

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Published

2025-03-23

How to Cite

Djite, A. S., & Seck, D. (2025). Shape stability of a quadrature surface problem in infinite Riemannian manifolds . International Journal of Maps in Mathematics, 8(1), 2–34. Retrieved from https://simadp.com/journalmim/article/view/184