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Research Results
MARCOS CRAIZER
RECENT PUBLICATIONS
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• Improper affine spheres. There is a strong connection between Area Distance and non-convex Improper Affine Spheres that was explored in [1] and [2]. In [5], one can find a classification of stable singularities of convex Improper Affine Spheres.
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• Volume distance to hypersurfaces. Although the Area Distance in the plane is an Improper Affine Sphere, this property does not hold in higher dimensions. Nevertheless, the volume distance have some nice affine differential properties [4].
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• Affine evolutes and symmetry sets. In [7], several properties of the Area Evolute and Center Symmetry Set are described. A discrete version of these results can be found in [6]. In [3], one can find a discrete version of the Affine Evolute, Affine Distance Symmetry Set. In the same paper there are discrete versions of the the Six Vertex Theorem and an affine isoperimetric inequality.
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1. Marcos Craizer, Moacyr Alvim, Ralph Teixeira: Area Distances of Convex Plane Curves and Improper Affine Spheres, SIAM Journal on Mathematical Imaging, 1(3), p.209-227, 2008.
2. Marcos Craizer, Ralph Teixeira, Moacyr Alvim: Affine properties of convex equal-area polygons, Discrete and Computational Geometry, 48(3), 580-595, 2012.
3. Marcos Craizer, Equiaffine Characterization of Lagrangian Surfaces in R^4, International Journal of Mathematics, 26(9), 1550074, 2015.
4. Marcos Craizer, Wojtek Domitrz, Pedro Rios: Even Dimensional Improper Affine Spheres, Journal of Mathematical Analysis and Applications, 421, 1803-1826, 2015.
5. Marcos Craizer, Ralph Teixeira, Vitor Balestro: Discrete cycloids from convex symmetric polygons, Discrete and Computational Geometry, 60, 859-884, 2018.
6. Marcos Craizer, Marcelo Saia, Luis Sánchez: Affine focal set of codimension 2 submanifolds contained in hypersurfaces, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 148A, 995-1016, 2018.
7. Marcos Craizer, Sinesio Pesco: Affine geometry of equal-volume polygons in 3-space, Computer Aided Geometric Design 57, 44-56, 2017.
8. Marcos Craizer, Sinesio Pesco: Centroaffine duality for spatial polygons, aceito para publicação no Discrete and Computational Geometry, 2019
9. Marcos Craizer, Ronaldo Garcia: Quadratic points of surfaces in projective 3-space, aceito para publicação no Quarterly Journal of Mathematics, 2019.
10. Marcos Craizer, Ronaldo Garcia: Centroaffine duality and Loewner’s type conjectures, pré-publicação, 2019. |
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(Updated 10/28/2019) |
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