正则抛物（双）利普希茨像的大块等价于抛物一致可求长性
Big Pieces of Regular Parabolic (bi-)Lipschitz Images is Equivalent to Parabolic Uniform Rectifiability
AI总结：
该研究定义正则抛物（双）利普希茨像概念，将David-Semmes理论推广到抛物语境，证明抛物Ahlfors-David正则集的抛物一致可求长性等价于其具有n维时空的抛物（双）利普希茨像的大块。
AI中文摘要：
我们定义正则抛物（双）利普希茨像的概念：它是n维时空上的抛物（双）利普希茨映射，经平移后保持t变量固定，且空间分量均为正则抛物利普希茨函数。我们证明，任意抛物Ahlfors-David正则集是抛物一致可求长集，当且仅当它具有n维时空的抛物利普希茨像的大块，当且仅当它具有n维时空的抛物双利普希茨像的大块。这将David-Semmes理论进一步推广到抛物语境。我们的证明结合了第一作者此前工作[BH12,BHH+22]的思路，以及Azzam和Schul[AS12]的部分思路；该证明可轻松适配（且远不那么复杂）到欧氏情形，以给出类似事实的另一种证明。
英文摘要：
We define the notion of regular parabolic (bi-)Lipschitz images as the parabolic (bi-)Lipschitz maps from $n$-dimensional space time which, up to translation, fix the $t$ variable and whose spatial components are each regular parabolic Lipschitz functions. We show that any parabolic Ahlfors-David regular is parabolic uniformly rectifiable if and only if it has big pieces of parabolic Lipschitz images of $n$-dimensional space time if and only if it has big pieces of parabolic bi-Lipschitz images of $n$-dimensional space time. This further extends the David-Semmes theory to the parabolic setting. Our proof combines the ideas of the first authors previous work [BH12,BHH+22] and some ideas of Azzam and Schul [AS12]. The proof easily adapts (and is far less complicated) to the Euclidean case to give an alternative proof of the analogous fact.
