Below you can find a list of my publications. They are not necessarily in chronological order. Papers that appear as “in preparation” are in an advanced stage of preparation, and therefore are most likely to be indeed submitted. Click in the names of the papers for respective links and comments. For all the arXiv versions just click in this link. Please get in touch for any doubts/informations/comments/suggestions!

V. Balestro, H. Martini and R. Teixeira:* Convexity From the Geometric Point of View*. Book in preparation, final version expected to December 2020. Please get in touch if you want to receive a preliminary version!

V. Balestro, B. Santiago e R. Teixeira: *Análise Funcional (livro em preparação)*.*

* *This is a textbook on basic Functional Analysis written in Portuguese language. We expect to have the final version in the ending of 2020.*

V. Balestro, H. Martini and R. Teixeira: *A new approach to Cauchy’s surface area formula*, 2020.

V. Balestro, H. Martini and R. Teixeira: *Convex analysis in normed spaces and metric projections onto convex bodies*, 2019.

V. Balestro, H. Martini and R. Teixeira: *Duality of gauges and symplectic forms in vector spaces*, Collectanea Mathematica, 2020.

V. Balestro, H. Martini and R. Teixeira: *Differential geometry of immersed surfaces in three-dimensional normed spaces*, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2020.

V. Balestro, H. Martini and M. Sakaki: *Differential geometry of spatial curves for gauges*, São Paulo Journal of Mathematical Sciences, 2020.

D. Sain, S. Roy, S. Bagchi and V. Balestro:* A study of symmetric points in Banach spaces*, Linear Multilinear Algebra, 2020.

V. Balestro, H. Martini and R. Teixeira: *Some topics in differential geometry of normed spaces*, Adv. Geom., 2020.

V. Balestro, H. Martini and R. Teixeira: *On curvature of surfaces immersed in normed spaces*, Monatsh. Math. **192**, pp. 291-309, 2020.

V. Balestro, H. Martini and M. Sakaki: *Curvature types of curves for planar gauges*, J. Geom. **111**, article 12, 2020.

V. Balestro, H. Martini and R. Teixeira: *Asymmetry measures for convex distance functions*, J. Convex Anal. **27**, pp. 117-138, 2020.

V. Balestro, Á. Horváth and H. Martini: *The inverse problem on roulettes in normed planes*, Anal. Math. Phys. **9**, pp. 2413-2434, 2019.

V. Balestro, H. Martini and E. Shonoda: *Concepts of curvature in normed planes*, Expo. Math. **37(4)**, pp. 347-381, 2019.

V. Balestro, H. Martini and R. Teixeira: *A new geometric view on Sturm-Liouville eigenvalue problems*, Monatsh. Math. **190(2)**, pp. 213-236, 2019.

V. Balestro, H. Martini and R. Teixeira: *Surface immersions in normed spaces from the affine point of view**,* Geom. Dedicata **201(1)**, pp. 21-31, 2019.

V. Balestro and H. Martini: *The Rosenthal-Szasz inequality for normed planes**,* Bull. Aust. Math. Soc. **99**, pp. 130-136, 2019.

V. Balestro, H. Martini and R. Teixeira: *Optimal constants in normed planes*, J. Convex Anal. **26(1)**, pp. 89-104, 2019.

V. Balestro, H. Martini and R. Teixeira: *On Legendre curves in normed planes*, Pacific J. Math. **297**, pp. 1-27, 2018.

M. Craizer, R. Teixeira and V. Balestro: *Discrete cycloids from convex symmetric polygons*, Discrete Comput. Geom. **60(4)**, pp. 859-884, 2018.

M. Craizer, R. Teixeira and V. Balestro: *Closed cycloids in a normed plane*, Monatsh. Math. **185(1)**, pp. 43-60, 2018.

V. Balestro, H. Martini and R. Teixeira: *Geometric constants for quantifying the difference between orthogonality types*, Ann. Funct. Anal. **7(4)**, pp. 656-671, 2016.

V. Balestro, Á. G. Horváth, H. Martini and R. Teixeira: *Angles in normed spaces*, Aequat. Math. **91(2)**, pp. 201-236, 2017.

V. Balestro and E. Shonoda: *On a cosine function defined for smooth normed spaces*, J. Convex Anal. **25(1)**, pp. 21-39, 2018.

V. Balestro, H. Martini and R. Teixeira: *Geometric properties of a sine function extendable to arbitrary normed planes*, Monatsh. Math. **182(4)**, pp. 781-800, 2017.

V. Balestro, Á. G. Horváth and H. Martini: *Angle measures, general rotations, and roulettes in normed planes*, Anal. Math. Phys. **7(4)**, pp. 549-575, 2017.

V. Balestro, H. Martini and R. Teixeira: *A new construction of Radon curves and related topics*, Aequat. Math. **90(5)**, pp. 1013-1024, 2016.

V. Balestro: *Curvature motion in time-dependent Minkowski planes*, Int. Elect. J. Geom. **8(2)**, pp. 70-81, 2015.

V. Balestro, H. Martini and R. Teixeira: **Hausdorff distances and Steiner symmetrizations in Banach spaces**, 2019.

G. Guedes, V. Balestro, D. Palma and A. Gonçalves: **The Doppler broadening phenomena revisited: mathematical aspects**, 2019.

V. Balestro: **Geometry of billiards in normed planes**, 2019(?).

V. Balestro and H. Martini: **What is Minkowski geometry, and why to study it?**, 2019 (expository paper).

V. Balestro, H. Martini and R. Teixeira: **Differential Geometry of Normed Spaces**, 2019 (book).

V. Balestro, H. Martini and R. Teixeira: **Trigonometric functions for convex distance functions**, 2019(?).