A critical set with nonnull image has large Hausdorff dimension-Reference-Cited by-同舟云学术

A critical set with nonnull image has large Hausdorff dimension

Published:1986 Issue:1 Volume:296 Page:367-376
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Norton Alec

Abstract

The question of how complicated a critical set must be to have a nonnull image is answered by relating its Hausdorff dimension to the (Hölder) differentiability of the map. This leads to a new extension of the Morse-Sard Theorem. The main tool is an extended version of Morse’s Lemma.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1986-296-01/S0002-9947-1986-0837817-2/S0002-9947-1986-0837817-2.pdf

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