Extending and correcting some research results on minimal and harmonic surfaces

In this article, we give necessary and beneficial extension for several important theorems by Monterde et al. on minimal and harmonic surfaces, so that they can be applied to all generic situations for n×mn×m (n≠mn≠m or n=mn=m) Bézier surfaces, instead of the special case of n×nn×n Bézier surfaces. At the same time, we point out the errors in Monterde et al.ʼs six papers, and give the correct and precise answers.

► We give extension for several important theorems on minimal and harmonic surfaces. ► They can be applied to all generic situations for n×mn×m Bézier surfaces. ► And we point out the errors seriatim and give the correct and precise answers.