标题： 标量曲率刚性的扭曲乘积度量 显示英文标题

标题： Scalar curvature rigidity of warped product metrics

摘要： 我们展示了在紧区间上配备严格对数凹凸的扭曲函数的圆球的扭曲积的标量平均曲率刚性。 这推广了Cecchini-Zeidler的早期结果到所有维度。 此外，我们证明了移除两个对径点后的至少3维圆球的标量曲率刚性。 这解决了Gromov的“四次讲座”中的一个问题在所有维度上。 我们的论证基于自旋几何。 显示英文摘要

摘要： We show scalar-mean curvature rigidity of warped products of round spheres of dimension at least 2 over compact intervals equipped with strictly log-concave warping functions. This generalizes earlier results of Cecchini-Zeidler to all dimensions. Moreover, we show scalar curvature rigidity of round spheres of dimension at least 3 with two antipodal points removed. This resolves a problem in Gromov's ''Four Lectures'' in all dimensions. Our arguments are based on spin geometry.