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The equivalence of strict convexity and injectivity of the gradient in bounded level sets

✍ Scribed by Andreas Griewank; Hubertus Th. Jongen; Man Kam Kwong


Publisher
Springer-Verlag
Year
1991
Tongue
English
Weight
272 KB
Volume
51
Category
Article
ISSN
0025-5610

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Convexity in x of the level sets of the
✍ Chie-Ping Chu πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 168 KB

## Abstract On a planar domain which is convex in __x__, the level sets of the first Dirichlet eigenfunction for Laplacian are also convex in __x__. This gives an affirmative answer to a conjecture proposed by B. Kawohl. (Β© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)