Armstrong, Niles2019-04-182019-04-182019-05-01http://hdl.handle.net/2097/39621The mean value theorem for harmonic functions has historically been an important and powerful result. As such, a generalization of this theorem that was stated by Caffarelli in 1998 and later proved by Blank-Hao in 2015 is of immediate interest. However, in order to make more use of this new general mean value theorem, more information about the mean value sets that appear in the theorem is needed. We present here a few new results regarding properties of such mean value sets.en-US© the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).http://rightsstatements.org/vocab/InC/1.0/Mean Value SetsMean Value TheoremDissertation