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| ON THE RECOVERY OF A CURVE ISOMETRICALLY IMMERSED IN ${\mathbb E}^n$ |
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Citation： |
M. SZOPOS.ON THE RECOVERY OF A CURVE ISOMETRICALLY IMMERSED IN ${\mathbb E}^n$[J].Chinese Annals of Mathematics B,2004,25(4):507~522 |
| Page view： 1269
Net amount： 890 |
Authors： |
M. SZOPOS; |
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| Abstract： |
It is known from classical differential geometry that one can
reconstruct a curve with $(n-1)$ prescribed curvature functions,
if these functions can be differentiated a certain number of times
in the usual sense and if the first $(n-2)$ functions are strictly
positive. It is established here that this result still holds
under the assumption that the curvature functions belong to some
Sobolev spaces, by using the notion of derivative in the
distributional sense. It is also shown that the mapping which
associates with such prescribed curvature functions the
reconstructed curve is of class ${\cal C}^\infty$. |
Keywords： |
Differential geometry, Nonlinear elasticity, Curves in Euclidean space,Frenet equations, Weak derivatives |
Classification： |
53A04, 34G05, 74K05 |
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