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Total curvature and area of curves with cusps and of surface maps.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
2005 (English)In: Mathematica Scandinavica, ISSN 0025-5521, Vol. 96, no 2, 224-242 p.Article in journal (Refereed) Published
Abstract [en]

A curvature-area inequality for planar curves with cusps is derived. Using this inequality, the total (Lipschitz-Killing) curvature of a map with stable singularities of a closed surface into the plane is shown to be bounded below by the area of the map divided by the square of the radius of the smallest ball containing the image of the map. This latter result fills the gap in Santalo's [7] proof of a similar estimate for surface maps into R-n, n > 2.

Place, publisher, year, edition, pages
2005. Vol. 96, no 2, 224-242 p.
Keyword [en]
Differential Geometry
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-3274ISI: 000232325700005Local ID: 3480OAI: oai:DiVA.org:miun-3274DiVA: diva2:28306
Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2011-04-06Bibliographically approved

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