论文标题
Lipschitz的连续性和Bochner-Eells-Sampson不平等，用于谐波地图的$ \ mathrm {rcd}（k，n）$ spaces to $ \ mathrm {cat}（0）$ space
Lipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from $\mathrm{RCD}(K,N)$ spaces to $\mathrm{CAT}(0)$ spaces
论文作者
论文摘要
我们从$ \ mathrm {rcd}（k，n）$ conrm {rcd}（k，n）$公制曲率范围和尺寸上限的谐波规律性从$ \ mathrm {cat}（cat}（0）具有非稳态截面曲率的$ \ mathrm {cat}（0）。在相同的假设下，我们获得了Hessian类型期的Bochner-Eells-Sampson不平等。这为平滑源和目标空间的经典理论提供了相当完整的概括，并对其自然合成对应物进行了肯定的答案，并对最近的文献中提出了多次提出的问题。 这些证明是基于对源空间上最佳传输与热流之间的相互作用的新解释，以及pdes粘度理论精神的原始扰动论点。
We establish Lipschitz regularity of harmonic maps from $\mathrm{RCD}(K,N)$ metric measure spaces with lower Ricci curvature bounds and dimension upper bounds in synthetic sense with values into $\mathrm{CAT}(0)$ metric spaces with non-positive sectional curvature. Under the same assumptions, we obtain a Bochner-Eells-Sampson inequality with a Hessian type-term. This gives a fairly complete generalization of the classical theory for smooth source and target spaces to their natural synthetic counterparts and an affirmative answer to a question raised several times in the recent literature. The proofs build on a new interpretation of the interplay between Optimal Transport and the Heat Flow on the source space and on an original perturbation argument in the spirit of the viscosity theory of PDEs.
