An example of a C1-smooth function whose gradient range is an arc with no tangent at any point.
Korobkov, M.V.
Sibirskij Matematicheskij Zhurnal, Tome 49 (2008), p. 134-144 / Harvested from The Electronic Library of Mathematics
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Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:55608 
@article{05381040,
     title = {An example of a },
     journal = {Sibirskij Matematicheskij Zhurnal},
     volume = {49},
     year = {2008},
     pages = {134-144},
     zbl = {1164.26323},
     language = {en},
     url = {http://dml.mathdoc.fr/item/05381040}
}

Korobkov, M.V. An example of a . Sibirskij Matematicheskij Zhurnal, Tome 49 (2008) pp. 134-144. http://gdmltest.u-ga.fr/item/05381040/