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 and a non-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.

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.

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

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

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

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

Thanks.

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 and a non-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.