Cadoi
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Registered User
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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. |
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Jan 13 |
awarded | ● Supporter |
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Jan 13 |
revised |
Known size invariant for Riemannian manifolds? deleted 40 characters in body |
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Jan 13 |
revised |
Known size invariant for Riemannian manifolds? added 202 characters in body |
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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 $K \subset M$. |
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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. |
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Jan 13 |
revised |
Known size invariant for Riemannian manifolds? added 149 characters in body; added 118 characters in body |
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Jan 12 |
awarded | ● Editor |
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Jan 12 |
revised |
Known size invariant for Riemannian manifolds? edited body |
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Jan 12 |
awarded | ● Student |
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Jan 12 |
asked | Known size invariant for Riemannian manifolds? |
