Yamabe product conjecture for Mn−1×S1M^{n-1}\times S^1Mn−1×S1 and S2×T2S^2\times T^2S2×T2
Yamabe product conjecture. The Yamabe constant Y(g(T))Y(g(T))Y(g(T)) is minimized by un,Tu_{n,T}un,T, and
The Strichartz conjecture on the real line times the three-sphere
The Strichartz conjecture on R×S3\mathbb{R}\times\mathbb{S}^3R×S3. One has