The geometry of total curvature on complete open surfaces - Shiohama, K. (Katsuhiro), 1940- (Cambridge tracts in mathematics, 2003)
A self-contained account of how modern differential geometry can be used to tackle and extend classical results in integral geometry. Open problems are provided, and the text is richly illustrated with figures to aid understanding and develop intuition. Suitable for graduate students and non-specialists seeking an introduction to this area.