Generalized solutions of curvature equations

✍ Scribed by Kazuhiro Takimoto

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 294 KB
• Volume: 67
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2006.07.014

✦ Synopsis

We introduce a notion of "generalized solutions" for the so-called curvature equations. It is an extension of the definition of generalized solutions of the Gauss curvature equation and gives a new framework for the study of more general curvature equations. We prove that if the curvature equation has a convex solution, then the inhomogeneous term must be a Borel measure. We also discuss basic properties of generalized solutions. Among other things, we show that our class of generalized solutions is wider than that of weak solutions.