标题： 散度形式下的黎曼流形上的Serrin型问题 显示英文标题

标题： Serrin-type problem in divergence form on Riemannian manifolds

摘要： 在本文中，我们研究了在具有非负 Ricci 曲率的黎曼流形中的有界区域上的发散型超定边界值问题。 使用积分恒等式和$P$-函数方法，我们推导出几何不等式和刚性结果。 在非线性项上的自然条件下，我们证明等号成立时区域与欧几里得球面等距，从而将经典的对称性结果扩展到黎曼情形。 显示英文摘要

摘要： 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.