arXiv subjects

Joyce Sindeaux

Publications and source records attributed to Joyce Sindeaux.

3 recordsLinked to original sources

arXiv2025

Serrin-type problem in divergence form on Riemannian manifolds

In this paper, we investigate an overdetermined boundary value problem of divergence type on bounded domains in Riemannian manifolds with non-negative Ricci curvature. Using integral identities and the $P$-function method, we derive geometric inequalities and rigidity results. Under natural conditions on the nonlinearity, we prove that equality implies the domain is isometric to a Euclidean ball, thereby extending classical symmetry results to the Riemannian setting.

math.DG↗

arXiv2025

Rigidity of Serrin-type problems via integral identities

In this short note, we deal with Serrin-type problems in Riemannian manifolds. Firstly, we provide a Soap Bubble type theorem and rigidity results. In another direction, we obtain a rigidity result addressed to annular regions in Einstein manifolds endowed with a conformal vector field.

math.DG↗

arXiv2025

Serrin's type Problems in convex cones in Riemannian manifolds

In this work, we discuss several results concerning Serrin's problem in convex cones in Riemannian manifolds. First, we present a rigidity result for an overdetermined problem in a class of warped products with Ricci curvature bounded below. As a consequence, we obtain a rigidity result for Einstein warped products. Next, we derive a soap bubble result and a Heintze-Karcher inequality that characterize the intersection of geodesic balls with cones in these spaces. Finally, we analyze the analogous ovedetermined problem for the drift Laplacian, where the ambient space is a cone in the Euclidean space.

math.DG↗