Brouwer's fixed-point theorem and a generalization of the formula for change of variables in multiple integrals (Q1310377)
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scientific article; zbMATH DE number 480449
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Brouwer's fixed-point theorem and a generalization of the formula for change of variables in multiple integrals |
scientific article; zbMATH DE number 480449 |
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Brouwer's fixed-point theorem and a generalization of the formula for change of variables in multiple integrals (English)
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17 August 1995
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The author proves that the Jacobian change of variable formula for multiple integrals remains true for maps that are not one-to-one, if the boundaries are preserved diffeomorphically. Applying this fact he gives a simple proof for the non-existence of a smooth retract of an embedded compact \(n\)-dimensional manifold with boundary onto its boundary. This allows him to derive a simple analytic proof for Brouwer's fixed point theorem.
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Jacobian change of variable formula for multiple integrals
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non-existence of a smooth retract of an embedded compact \(n\)-dimensional manifold
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analytic proof for Brouwer's fixed point theorem
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