Asian Journal of Mathematics

Volume 25 (2021)

Number 3

Segre’s theorem. An analytic proof of a result in differential geometry

Pages: 321 – 340



Karl K. Brustad (Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway)


We present an analytic approach on how to solve the overdetermined problem $\lvert \nabla u \rvert = f(u), \Delta u = g(u)$, in connected domains $\Omega \subseteq \mathbb{R}^n$.


isoparametric, viscosity, eigenprojections, $1$-Laplacian, matrix derivatives, Cartan’s fundamental formula

2010 Mathematics Subject Classification

35C05, 35J60, 53A05

The author was supported by the Academy of Finland (grant SA13316965), and by Aalto University.

Received 13 August 2020

Accepted 28 August 2020

Published 14 March 2022