Critical Points and Level Sets of Grushin-Harmonic Functions in the Plane

Author(s):  
Hairong Liu ◽  
Xiaoping Yang
2002 ◽  
Vol 40 (2) ◽  
pp. 335-362 ◽  
Author(s):  
Anders Öberg ◽  
Robert S. Strichartz ◽  
Andrew Q. Yingst

1977 ◽  
Vol 29 (4) ◽  
pp. 707-721
Author(s):  
Paul A. Vincent

One aspect of topological analysis that authors, such as G. T. Whyburn and Marston Morse, have pointed to ([16; 6] for instance) as being fundamental in the development of function theory is the topological study of the level sets of analytic and harmonic functions or of their topological analogues, light open maps and pseudo-harmonic functions. The first step in this direction seems to have been made by H. Whitney [14] when he studied families of curves, given abstractly using a condition of regularity.


2016 ◽  
Vol 18 (03) ◽  
pp. 1650010
Author(s):  
Lizhou Wang

We construct three families of singular critical points for a variational free boundary problem. These critical points are homogeneous solutions of degree one to some overdetermined boundary value problem. The intersections of the level sets of these solutions with the unit sphere are isoparametric hypersurfaces and their focal submanifolds.


2009 ◽  
Vol 58 (4) ◽  
pp. 1947-1970 ◽  
Author(s):  
Alberto Enciso ◽  
Daniel Peralta-Salas

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