Geodesic
The parametric Weierstrass integral over a BV curve as a length functional
Studia Mathematica, Tome 127 (1998) no. 1, pp. 9-19

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The constructive definition of the Weierstrass integral through only one limit process over finite sums is often preferable to the more sophisticated definition of the Serrin integral, especially for approximation purposes. By proving that the Weierstrass integral over a BV curve is a length functional with respect to a suitable metric, we discover a further natural reason for studying the Weierstrass integral. This characterization was conjectured by Menger.
DOI : 10.4064/sm-127-1-9-19

Loris Faina 1

1 
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Loris Faina. The parametric Weierstrass integral over a BV curve as a length functional. Studia Mathematica, Tome 127 (1998) no. 1, pp. 9-19. doi: 10.4064/sm-127-1-9-19

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