Implicit Equations of the Henneberg-Type Minimal Surface in the Four-Dimensional Euclidean Space

Round 1

Reviewer 1 Report

The manuscript entitled “Implicit Equation of the Henneberg-Type Minimal Surface in the Four Dimensional Euclidean Space” has described a two parameter family of Henneberg-type minimal surface for positive integers m, n using the Weierstrass representation in the four dimensional Euclidean space E4. Furthermore, the authors have obtained obtain implicit algebraic equation of the Henneberg-type minimal surface of values 4, 2.  According to this reviewer, the present work will be beneficial to researcher working in this field and could be accepted after address following comments/suggestions.

They are:

Please check the manuscript for typographical errors.

Some important and relevant references are missing. For better understanding these references should be cited and discussed in the main body of the manuscript (ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA 2016, 20, 123 DOI: 10.12697/ACUTM.2016.20.11; Computers & Structures 2015, 161, 55-63 DOI: 10.1016/j.compstruc.2015.09.002)

Author Response

We checked paper and rewrote considering reviewer’s comments.

Author Response File: Author Response.pdf

Reviewer 2 Report

Referee report

“Implicit Equation of the Henneberg-Type Minimal Surface in the Four Dimensional Euclidean Space”

This work is an extension of the authors own work (ref.7) to Henneberg type surfaces. The main new finding is the surface algebraic index of (4,2). I recommend publication of the work after minor revisions:

(a Extend abstract to double length with a more descriptive context.

(b Extend the introduction.

(c If the author want to improve the paper they can give an interpretation of the double-integer-index derived in the paper, especially a geometrical understanding of the involved surfaces would be helpful. 

Recomadation: Reconsider after major revision.

Author Response

We checked and revised paper considering reviewer’s comments.

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper is devoted to the determination of Henneberg-type minimal surfaces in $E^4$ by means of the Weierstrass representation.. 

The paper is just a sequel of long formulae (and a huge formula not completely displayed on page 5), some derived with the aid of Maple system. 

The paper could be interesting as a contribution to the "zoological" classification of minimal surfaces, and no new general idea is proposed. My opinion is that a mathematical paper can not reduce only to a sequence of formulae.

Besides these general considerations,  some comments are in order:

1) the abstract does not clarify to the reader the content of the paper (the integers m, n are not defined, even if one can understand their meaning in reading the paper).

2) the Section 1, that usually in a paper introduces the problem to be investigated and the notation, needs a deep rewriting.

3) a concluding section presenting the perspectives should be present. 

Nevertheless, the paper can be accepted after a revision where the three items above are suitably addressed.

Author Response

We checked and revised paper considering reviewer’s comments.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors have improved the paper, the introduction and the referencing. A clear cut transparent interpretation of the meaning of the indexes of value 4 and 2 would significant enhance the contribution of this paper.

Author Response

The authors have improved the paper, the introduction and the referencing. A clear cut transparent interpretation of the meaning of the indexes of value 4 and 2 would significant enhance the contribution of this paper.

We checked and add some interpretation, definition ect. in the abstract, introduction and section 3, considering the reviewer's above comments.

Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

Manuscript improved