发表机构
Massachusetts Institute of Technology（麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对正曲率爱因斯坦流形的格林函数，证明了其尖锐黑塞不等式及相关单调性公式，扩展了Park的结果，并给出几何应用。
AI 中文摘要
我们证明了具有正截面曲率的爱因斯坦流形的自然比较格林函数的尖锐黑塞不等式，该不等式可视为黑塞比较定理的格林函数类似物，也是热方程矩阵李-姚-汉密尔顿（matrix Li-Yau-Hamilton）不等式的正曲率椭圆对应物。我们还表明该不等式与一族单调性公式密切相关，将Park的先前结果扩展到正曲率情形。我们进一步给出若干几何应用，例如两个不同格林距离函数之和的尖锐比较不等式。
英文摘要
We prove a sharp Hessian inequality for the natural comparison Green's function of an Einstein manifold with positive sectional curvature, which may be viewed as a Green's function analogue of the Hessian comparison theorem and as a positively-curved, elliptic counterpart to the matrix Li-Yau-Hamilton inequality for the heat equation. We also show that this inequality is closely related to a family of monotonicity formulae, extending previous results of Park to the setting of positive curvature. We further present several geometric applications, such as a sharp comparison inequality for the sum of two distinct Green's distance functions.
Comments24 pages
