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A Riemannian Extension of a Quadrature Surface Free Boundary Problem: Stability and Optimality
We study a quadrature surface free boundary problem on a smooth compact finite-dimensional Riemannian manifold $(M,g)$. The problem is formulated as a shape optimization problem involving a Dirichlet problem for the Laplace--Beltrami operator, with a geometric condition on the free boundary. Under
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