@inbook{c5e8182b19ce4d659fa76daf58a934e0,
title = "Short-Time Existence",
abstract = "An important foundational step in the study of any system of evolutionary partial differential equations is to show short-time existence and uniqueness. For the Ricci flow, unfortunately, short-time existence does not follow from standard parabolic theory, since the flow is only weakly parabolic. To overcome this, Hamilton's seminal paper [Ham82b] employed the deep Nash –Moser implicit function theorem to prove short-time existence and uni- queness. A detailed exposition of this result and its applications can be found in Hamilton's survey [Ham82a]. DeTurck [DeT83]later found a more direct proof by modifying the flow by a time-dependent change of variables to make it parabolic. It is this method that we will follow.",
keywords = "Bianchi Identity, Geometric Invariance, Principal Symbol, Ricci Flow, Ricci Tensor",
author = "Ben Andrews and Christopher Hopper",
note = "Publisher Copyright: {\textcopyright} 2011, Springer-Verlag Berlin Heidelberg.",
year = "2011",
doi = "10.1007/978-3-642-16286-2_5",
language = "English",
isbn = "9783642159664",
series = "Lecture Notes in Mathematics",
publisher = "Springer Verlag",
pages = "83--95",
booktitle = "The Ricci Flow in Riemannian Geometry",
address = "Germany",
}