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Deane Yang
Deane Yang
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It is well known that Heisenberg groups cannot be bi-Lipschitz embedded into Euclidean spaces. A standard proof uses the fact that a Lipschitz mapping from a Heisenberg group into a Euclidean space is almost everywhere Pansu differentiable. Do you know proofs of this result that do not use Pansu differnetiabilitydifferentiability? I have heard that there are such proofs, but I do not know where to find them.

EDIT: I like all three answers of rob, Robert Young and YCor so I cannot accept any of them since I would like to accept each of them.

It is well known that Heisenberg groups cannot be bi-Lipschitz embedded into Euclidean spaces. A standard proof uses the fact that a Lipschitz mapping from a Heisenberg group into a Euclidean space is almost everywhere Pansu differentiable. Do you know proofs of this result that do not use Pansu differnetiability? I have heard that there are such proofs, but I do not know where to find them.

EDIT: I like all three answers of rob, Robert Young and YCor so I cannot accept any of them since I would like to accept each of them.

It is well known that Heisenberg groups cannot be bi-Lipschitz embedded into Euclidean spaces. A standard proof uses the fact that a Lipschitz mapping from a Heisenberg group into a Euclidean space is almost everywhere Pansu differentiable. Do you know proofs of this result that do not use Pansu differentiability? I have heard that there are such proofs, but I do not know where to find them.

EDIT: I like all three answers of rob, Robert Young and YCor so I cannot accept any of them since I would like to accept each of them.

added 138 characters in body; edited title
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Piotr Hajlasz
Piotr Hajlasz
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Embedding Non embedding of the Heisenberg group

It is well known that Heisenberg groups cannot be bi-Lipschitz embedded into Euclidean spaces. A standard proof uses the fact that a Lipschitz mapping from a Heisenberg group into a Euclidean space is almost everywhere Pansu differentiable. Do you know proofs of this result that do not use Pansu differnetiability? I have heard that there are such proofs, but I do not know where to find them.

EDIT: I like all three answers of rob, Robert Young and YCor so I cannot accept any of them since I would like to accept each of them.

Embedding of the Heisenberg group

It is well known that Heisenberg groups cannot be bi-Lipschitz embedded into Euclidean spaces. A standard proof uses the fact that a Lipschitz mapping from a Heisenberg group into a Euclidean space is almost everywhere Pansu differentiable. Do you know proofs of this result that do not use Pansu differnetiability? I have heard that there are such proofs, but I do not know where to find them.

Non embedding of the Heisenberg group

It is well known that Heisenberg groups cannot be bi-Lipschitz embedded into Euclidean spaces. A standard proof uses the fact that a Lipschitz mapping from a Heisenberg group into a Euclidean space is almost everywhere Pansu differentiable. Do you know proofs of this result that do not use Pansu differnetiability? I have heard that there are such proofs, but I do not know where to find them.

EDIT: I like all three answers of rob, Robert Young and YCor so I cannot accept any of them since I would like to accept each of them.

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Piotr Hajlasz
Piotr Hajlasz
  • 28k
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Embedding of the Heisenberg group

It is well known that Heisenberg groups cannot be bi-Lipschitz embedded into Euclidean spaces. A standard proof uses the fact that a Lipschitz mapping from a Heisenberg group into a Euclidean space is almost everywhere Pansu differentiable. Do you know proofs of this result that do not use Pansu differnetiability? I have heard that there are such proofs, but I do not know where to find them.