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Abstract
In Euclidean 3space endowed with a Cartesian reference system, we consider a class of surfaces, called Delaunay tori, constructed by bending segments of Delaunay cylinders with necksize a and n lobes along circumferences centered at the origin. Such surfaces are complete and compact, have genus one and almost constant, say 1, mean curvature, when n is large. Considering a class of mappings H: (Formula presented) (Formula presented) such that H(X) 1 as X (Formula presented) with some decay of inversepower type, we show that for n large and  a small, in a suitable neighborhood of any Delaunay torus with n lobes and necksize a there is no parametric surface constructed as normal graph over the Delaunay torus and whose mean curvature equals H at every point.
Original language  English 

Pages (fromto)  193252 
Number of pages  60 
Journal  Advances in Differential Equations 
Volume  27 
Issue number  34 
Early online date  7 Feb 2022 
Publication status  Published  31 Mar 2022 
Bibliographical note
Funding Information:The first and the second author are members of the Gruppo Nazionale per ??Analisi Matematica, la Probabilit? e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The third author has been supported by EPSRC research GrantEP/T008 458/1. This paper has been written when the second author was at D?partement de Math?matique, Universit? Libre de Bruxelles and was also supported by FNRSF.R.S.
Funding Information:
The third author has been supported by EPSRC research GrantEP/T008 458/1. This paper has been written when the second author was at Département de Mathématique, UniversitéLibre de Bruxelles and was also supported by FNRSF.R.S.
ASJC Scopus subject areas
 Analysis
 Applied Mathematics
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Concentration phenomena in nonlinear analysis
Engineering and Physical Sciences Research Council
27/04/20 → 31/07/24
Project: Research council