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Jan
14
comment Known size invariant for Riemannian manifolds?
@alvarezpaiva: I should have included the source of this invariant from the start to be fair to Irie as well as any readers. I was/am in particular looking for other Riemannian geometry connections to this invariant, as opposed to the symplectic connection, so I thought I could steer the question towards the Riemannian side by not mentioning the symplectic side. This was a mistake and I am sorry.
Jan
13
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Jan
13
revised Known size invariant for Riemannian manifolds?
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Jan
13
revised Known size invariant for Riemannian manifolds?
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Jan
13
comment Known size invariant for Riemannian manifolds?
@Liviu Nicolaescu: This is why one specifies that $S_M(g)$ should be considered for open manifolds M. For non-open manifolds the best one can do is look at $S_M(g,K)$ for proper compact subsets $K \subset M$.
Jan
13
comment Known size invariant for Riemannian manifolds?
@Ubunke: Irie proves a non-trivial lower bound for $S_M(g)$ in terms of the displacement energy of the unit disk cotangent bundle $D^*M$ in $T^*M$. This is due to the symplectic view of this invariant mentioned by alvarezpaiva.
Jan
13
revised Known size invariant for Riemannian manifolds?
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Jan
12
awarded  Editor
Jan
12
revised Known size invariant for Riemannian manifolds?
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Jan
12
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Jan
12
asked Known size invariant for Riemannian manifolds?