The Non-compact Case
A closely related question is the so-called "non-compact Yamabe problem", which asks: on a smooth, complete Riemannian manifold (M,g) which is not compact, does there exist a conformal metric of constant scalar curvature that is also complete? The answer is no, due to counterexamples given by Jin (1988).
Read more about this topic: Yamabe Problem
Famous quotes containing the word case:
“Consider the deference which is everywhere paid to a doctor’s opinion. Nothing more strikingly betrays the credulity of mankind than medicine. Quackery is a thing universal, and universally successful. In this case it becomes literally true that no imposition is too great for the credulity of men.”
—Henry David Thoreau (1817–1862)
Related Phrases
Related Words