@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",

}