Today I read about Gromov's definition of minimal volume for smooth manifolds.

$$\min {\rm Vol}(M):=\inf_{|K_g|\leq1}\{{\rm Vol}(M,g)\}.$$

Gromov's conjecture states that for every closed simply connected odd-dimensional manifold $\min {\rm Vol}(M)=0$. Is the Gromov conjecture still open? Can anybody give an example for this conjecture?

**Update:** My teacher told to me that this conjecture can be solved by the Ricci flow method but I don't know how to use it. Can anybody give me an explanation to this? and how it works?

Thanks.

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