论文标题
在静态歧管上，满足边界上过度确定的罗宾类型条件
On static manifolds satisfying an overdetermined Robin type condition on the boundary
论文作者
论文摘要
在这项工作中，我们考虑了静态歧管$ m $，带有非空边界$ \ partial m $。在这种情况下，我们假设潜在的$ V $还满足了$ \ partial m $的过度确定的罗宾类型条件。我们证明了欧几里得封闭的单位球$ b^3 $ in $ \ mathbb {r}^3 $的刚性定理。更确切地说，当连接$σ$并相交$ \ partial m $时，我们为零集$σ= v^{ - 1}（0）$提供了一个清晰的上限。我们还考虑了$σ= v^{ - 1}（0）$不相交$ \ partial m $的情况。
In this work, we consider static manifolds $M$ with nonempty boundary $\partial M$. In this case, we suppose that the potential $V$ also satisfies an overdetermined Robin type condition on $\partial M$. We prove a rigidity theorem for the Euclidean closed unit ball $B^3$ in $\mathbb{R}^3$. More precisely, we give a sharp upper bound for the area of the zero set $Σ=V^{-1}(0)$ of the potential $V$, when $Σ$ is connected and intersects $\partial M$. We also consider the case where $Σ=V^{-1}(0)$ does not intersect $\partial M$.
