AN ESTIMATE FOR THE GAUSSIAN CURVATURE OF MINIMAL SURFACES IN EUCLIDEAN FOUR-SPACE WITH RAMIFICATION AN ESTIMATE FOR THE GAUSSIAN CURVATURE OF MINIMAL SURFACES IN EUCLIDEAN FOUR-SPACE WITH RAMIFICATION

DOI: 10.18173/2354-1059.2023-0020

Tóm tắt

In this article, we will establish an estimate for the Gaussian curvature of minimal surfaces in R4 whose classical Gauss map is ramified over the set of distinct points. This is a continuation of previous work of Fujimoto (1993, Aspect of Math., Vieweg, Wiesbaden, Vol. E21); Osserman-Ru (1997, J. Differ. Geom., Vol. 46, pp. 578-593) and Ha (2014, Differ. Geom. Appl., Vol. 32, pp. 130-138.)