Premium
The difference of topology at infinity in changingâsign Yamabe problems on đ 3 (the case of two masses)
Author(s) -
Bahri Abbas,
Chanillo Sagun
Publication year - 2001
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/1097-0312(200104)54:4<450::aid-cpa2>3.0.co;2-y
Subject(s) - mathematics , sign (mathematics) , infinity , topology (electrical circuits) , yamabe flow , mathematical analysis , pure mathematics , combinatorics , geometry , scalar curvature , sectional curvature , curvature
In this paper, we study the simplest cases of differences of topology at infinity in Yamabe-type problems with changing-sign solutions. In the past twenty years, there has been a wide range of activity in the study of the positive solutions to the problems of Yamabe-type, using various methods, including the study of differences of topology at infinity. After [1, 6], these differences of topology are starting to be well understood in the framework of positive functions. In sharp contrast to this, very little is known when the hypothesis of positivity is removed. We believe that completing such a task is important not only per se, but also because it lays the ground for Yang-Mills (Einsteinâs?) equations. These equations should only represent a complication in the background framework with respect to Yamabe changing-sign problems. In the present work, we are completing this program for the pure Yamabe problemâallowing for sign changesâon S3 and for only pairs of functions at infinity. In order to formulate our results, we need to introduce some notation and quote slight variations of well-known results. The partial differential equation that we will be studying is