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Martin Sleziak
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I am looking for applications of the notion of Gromov-Hausdorff convergence to prove theorems that a priori have nothing to do with it. Examples that I am aware of (thanks to wikipedia and google):

What are more examples? Ideally they would be along the lines of Gromov's theorem, or proofs of geometric facts, but I'm interested to hear about anything.

As a subquestion, are there interesting applications of Gromov's compactness theorem to prove results about manifolds with bounded Ricci which have nothing to do with GH convergence?

I am looking for applications of the notion of Gromov-Hausdorff convergence to prove theorems that a priori have nothing to do with it. Examples that I am aware of (thanks to wikipedia and google):

What are more examples? Ideally they would be along the lines of Gromov's theorem, or proofs of geometric facts, but I'm interested to hear about anything.

As a subquestion, are there interesting applications of Gromov's compactness theorem to prove results about manifolds with bounded Ricci which have nothing to do with GH convergence?

I am looking for applications of the notion of Gromov-Hausdorff convergence to prove theorems that a priori have nothing to do with it. Examples that I am aware of (thanks to wikipedia and google):

What are more examples? Ideally they would be along the lines of Gromov's theorem, or proofs of geometric facts, but I'm interested to hear about anything.

As a subquestion, are there interesting applications of Gromov's compactness theorem to prove results about manifolds with bounded Ricci which have nothing to do with GH convergence?

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Glorfindel
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I am looking for applications of the notion of Gromov-Hausdorff convergenceGromov-Hausdorff convergence to prove theorems that a priori have nothing to do with it. Examples that I am aware of (thanks to wikipedia and google):

What are more examples? Ideally they would be along the lines of Gromov's theorem, or proofs of geometric facts, but I'm interested to hear about anything.

As a subquestion, are there interesting applications of Gromov's compactness theoremGromov's compactness theorem to prove results about manifolds with bounded Ricci which have nothing to do with GH convergence?

I am looking for applications of the notion of Gromov-Hausdorff convergence to prove theorems that a priori have nothing to do with it. Examples that I am aware of (thanks to wikipedia and google):

What are more examples? Ideally they would be along the lines of Gromov's theorem, or proofs of geometric facts, but I'm interested to hear about anything.

As a subquestion, are there interesting applications of Gromov's compactness theorem to prove results about manifolds with bounded Ricci which have nothing to do with GH convergence?

I am looking for applications of the notion of Gromov-Hausdorff convergence to prove theorems that a priori have nothing to do with it. Examples that I am aware of (thanks to wikipedia and google):

What are more examples? Ideally they would be along the lines of Gromov's theorem, or proofs of geometric facts, but I'm interested to hear about anything.

As a subquestion, are there interesting applications of Gromov's compactness theorem to prove results about manifolds with bounded Ricci which have nothing to do with GH convergence?

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Otis Chodosh
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Applications of the notion of of Gromov-Hausdorff distance

I am looking for applications of the notion of Gromov-Hausdorff convergence to prove theorems that a priori have nothing to do with it. Examples that I am aware of (thanks to wikipedia and google):

What are more examples? Ideally they would be along the lines of Gromov's theorem, or proofs of geometric facts, but I'm interested to hear about anything.

As a subquestion, are there interesting applications of Gromov's compactness theorem to prove results about manifolds with bounded Ricci which have nothing to do with GH convergence?