Timeline for To what extent can one get rid of tangent lines and still have a continuous surface?
Current License: CC BY-SA 2.5
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| Apr 15, 2010 at 20:27 | comment | added | Garabed Gulbenkian | Let U be the non-empty open connected subset of the Cartesian x-y plane at all points of which F(x,y) is defined and continuous. What makes this problem difficult is that once having specified F(x,y), one then has to prove that no arc in R^3 with an equation of the form "x=g(t),y=h(t),z=F(g(t),h(t))-where t lies in the closure of (0,1)" has a tangent at any of its points, whenever x=g(t),y=h(t)is the equation of an arc lying in U. | |
| Mar 24, 2010 at 11:23 | comment | added | Petya | Your update is wrong. If $g$ is odd function then the surface $z=g(x)+g(y)$ contains a line. | |
| Mar 23, 2010 at 20:14 | history | edited | Yuri Bakhtin | CC BY-SA 2.5 |
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| Mar 23, 2010 at 19:59 | history | edited | Yuri Bakhtin | CC BY-SA 2.5 |
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| Mar 23, 2010 at 19:42 | history | answered | Yuri Bakhtin | CC BY-SA 2.5 |