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Dr.
Marcos Craizer
Associate Professor |
Biographical Information
Dr. Craizer received a B. degree in mathematics in 1983 from Federal
University of Rio de Janeiro (UFRJ), a M.Sc degree in 1985 and a Ph.D. degree
in 1989, both in mathematics at the Institute for Pure and Applied
Mathematics (IMPA).
Dr. Craizer is a professor at the Department of Mathematics of Pontifical Catholic University of Rio de Janeiro (PUC-Rio) since 1988.
Research Interests
- Affine and Projective Differential Geometry
- Discrete Geometry
Former Students
- Bruno Coelho Maciel - M.Sc. Dissertation:
Multi-resolution edge detection and image reconstruction from the edges,
- Marcilene Fátima Dianin-
M.Sc. Dissertation: Mathematical morphology, segmentation and curve
evolution,
- Decio Ângelo Fonini Jr.-
Ph.D. Thesis (co-advised with E.A.B.da Silva): Successive approximation
quantization,
- João Domingos Gomes da
Silva Jr. - M.Sc. Dissertation (co-advised with H.Lopes): Curvature
estimators based on parametric curve fitting,
- Cinthia de Oliveira
Lage Ferreira- M.Sc. Dissertation: Evolution of a union of balls from its
medial axis,
- Lhaylla dos Santos Cryssaff- Ph.D. Thesis: Geometric energies on triangulated surfaces, 17/02/2009.
- Paulo César Alves Araujo- M.Sc.Dissertation: Algumas Desigualdades Isoperimétricas para Curvas Planas, 28/04/2011.
- Marcelo Chaves Nascimento- M.Sc.Dissertation: Problemas Isoperimétricos no Plano de Minkowski, 23/03/2015.
- Ady Cambraia Junior- Ph.D.Thesis: Envelope of Mid-planes of Surfaces in R^3, 23/01/2015.
- Edison Fausto Cuba Huamani- M.Sc.Dissertation: Affine Minimal Surfaces with Singularities, 12/09/2017.
- Filipe Bellio da Nóbrega- M.Sc.Dissertation: Representation of generic curves by their singularities, 17/07/2018.
- Fernanda Py Silva Cordeiro- M.Sc.Dissertation: Comportamento das linhas de curvatura de uma superfície no 3-espaço euclidiano próximo a um ponto umbílico, 12/04/2019.
- Rafael Segadas dos Santos- Ph.D. Thesis: Cáusticas de Wigner e Conjuntos de Medida de Largura Constante em Planos Normados com Bolas Unitárias Suaves ou Poligonais, 2019.
- Samuel Pacitti Gentil- M.Sc.Dissertation: Aspectos Geométricos de Poligonais Genéricas: Curvatura Total e Convexidade, 2020.
- Anderson Reis de Vargas- Ph.D.Thesis: Asymptotic Nets with Constant Affine mean Curvature, 2021.
Publications
- Papers
- M.Craizer, Entropy of inner functions, Israel Journal of Mathematics, vol.74, 2-3, pp.129-168, 1991.
- M.Craizer, The Bernoulli property of inner functions. Ergodic Theory and Dynamical Systems, 12, p.209-215, 1992.
- J.L.Arraut,
M. Craizer, Stability of blocks of compact orbits of an action of R^2
on M^3. Advanced series in non-linear dynamics, 4,p.15-21,1993.
- M.Craizer, Homogenization of
codimension 1 actions of R^n near a compact orbit, Annales de L'Institut Fourier, vol.44,
n.5, pp.1435-1448, 1994.
- J.L.Arraut, M.Craizer, Foliations of
M^3 defined by R^2-actions, Annales de L'Institut Fourier, vol.45, n.4, pp.1091-1118,
1995.
- M.Craizer, E.A.B.da Silva and E.G.Ramos, New results on
successive approximation vector quantization, Electronics Letters IEE, vol.34, n.1.,
pp.59-60, 1998.
- M.Craizer, E.A.B.da Silva and E.G.Ramos, Convergent
algorithms for successive approximation vector quantization with
applications to wavelet image compression, IEE Proceedings - Vision, Image
and Signal Processing, vol. 146, n.3, pp 159-164, 1999.
- M.Craizer, A.O.Lopes, The
capacity-cost function of hard-constrained channels, International Journal of
Applied Mathematics, vol.2, n.10, pp. 1165-1180, 2000.
- M.Craizer, D.A.Fonini Jr. and E.A.B.da
Silva, Alpha-expansions: A class of frame decompositions, Applied and Computational
Harmonic Analysis, vol.13, pp.103-115, 2002.
- M.Craizer, D.A.Fonini Jr. and E.A.B.da
Silva, Successive approximation for image compression, IEEE Circuits and Systems
Magazine, vol.2,n.3, 3rd quarter, 2002.
- M.Craizer, Evolution of critical
points in curvature and affine morphological scale spaces, IV International
Conference on Scale-Space theories in Computer Vision,
- M.Craizer and R.Teixeira, Evolution of an
extremum by curvature motion, Journal of Mathematical Analysis and Applications, 293,
p.721-737, 2004.
- M.Craizer, S.Pesco and R.Teixeira, A numerical
scheme for the curvature equation near the singularities, Journal of Mathematical
Imaging and Vision, 22, p.89-95, 2005.
- M.Craizer, T.Lewiner, J.D.G.Silva Jr, H.C.V.Lopes. Curvature and Torsion Estimators based on Parametric Curve Fitting, Computer & Graphics, 29, n.5, 2005.
- T.Lewiner,
M.Craizer, H.Lopes, S.Pesco,L.Velho, E.Medeiros, GEncode:
Geometry-driven compression for general meshes. Computer Graphics
Forum, 25, p.685-695, 2006.
- T.Lewiner, C.Ferreira, M.Craizer,
R.Teixeira, Curvature Motion for
- M.Craizer,
T.Lewiner, J.M.Morvan, Combining points and tangents into parabolic
polygons, Journal of Mathematical Imaging and Vision, 29, p.131-140,
2007.
- M.A.H.B. da Silva, R.C.Teixeira, S.Pesco, M.Craizer, A Fast Marching Method for the Area based Affine Distance, Journal of Mathematical Imaging and Vision, 22(1), p.89-95, 2008.
- M.Craizer, M.A.H.B. da Silva, R.C.Teixeira, Area Distances of Convex Plane Curves and Improper Affine Spheres, SIAM Journal on Mathematical Imaging, 1(3), p.209-227, 2008.
- T.Lewiner, M.Craizer, Projective splines and estimators for planar curves, Journal of Mathematical Imaging and Vision, 36(1), p.81-89, 2010.
- M.Craizer, H.Anciaux, T.Lewiner, Discrete affine minimal surfaces with indefinite metric, Differential Geometry and its Applications, 28, 158-169, 2010.
- M.Craizer,
T.Lewiner, R. Teixeira, Cauchy problems for discrete affine minimal
surfaces, Archivum Mathematicum, 48(1), 1-14, 2012.
- M.Craizer,
R.Teixeira, M.da Silva, A geometric representation of improper
indefinite affine spheres with singularities, Journal of Geometry, 100(1), 65-78, 2011.
- M.Craizer, R.Teixeira, M.da Silva, Affine properties of convex equal-area polygons, Discrete and Computational Geometry, 48(3), 580-595,
2012.
- M.Craizer, R.C.Teixeira, Some properties of the volume distance to hypersurfaces, Differential Geometry and its Applications, 31, 510-516, 2013.
- M.Craizer, Singularities of Convex Improper Affine Maps, Journal of Geometry, 103(2), 207-217, 2012.
- M.Craizer, R.Teixeira, M.da Silva, Polygons with Parallel Opposite Sides, Discrete and Computational Geometry, 50(2), 474-490, 2013.
- M. Craizer, W.Domitrz, Pedro de M. Rios, Even Dimensional Improper Affine Spheres, Journal of Mathematical Analysis and Applications, 421, 1803-1826, 2015.
- M.Craizer, Iterates of Involutes of Constant Width Curves in the Mikowski Plane, Beiträge zur Algebra und Geometrie, 55(2), 479-496, 2014.
- M.Craizer and H.Martini, Involutes of Constant Width Polygons in the Minkowski Plane, Ars Mathematica Contemporanea, 11(1), 107-125, 2016.
- M.Craizer, Equiaffine Characterization of Lagrangian Surfaces in R^4, International Journal of Mathematics, 26(9), 1550074, 2015.
- M.Craizer, M.J.Saia and L.F.Sánchez, Equiaffine Darboux frames for codimension 2 submanifolds contained in hypersurfaces, J.Math.Soc.Japan, 69, n.4, p. 1331-1352, October 2017.
- Ady Cambraia Jr. and M.Craizer, Envelope of mid-planes of a surface and some classical notions of affine differential geometry, Results in Mathematics 72(4), 1865-1880, 2017.
- Ady Cambraia Jr. and M.Craizer, Envelope of Mid-Hyperplanes of a Hypersurface, Journal of Geometry 108(3), 899-911, 2017.
- M.Craizer, R.C.Teixeira and V.Balestro, Closed cycloids in a normed plane, Monatshefte fur Mathematik, 185(1), 43-60, 2017.
- M.Craizer, M.J.Saia and L.F.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.
- M.Craizer and S.Pesco, Affine geometry of equal-volume polygons in 3-space, Computer Aided Geometric Design 57, 44-56, 2017.
- M.Craizer, R.C.Teixeira and V.Balestro, Discrete cycloids from convex symmetric polygons, Discrete and Computational Geometry, 60, 859-884, 2018.
- M.Craizer and R.A.Garcia, Quadratic points of surfaces in projective 3-space, Quarterly Journal of Mathematics 70(3), 1105-1134, 2019.
- M.Barajas, M.Craizer and R.A.Garcia, Lines of affine principal curvature lines of surfaces in 3-space, Results in Mathematics, v.75, 32, 2020.
- M.Craizer, W.Domitrz, Pedro de M.Rios, Singular improper affine spheres from a given Lagrangian submanifold, Advances in Mathematics, v.374, 107326, 2020.
- M.Craizer and R.A.Garcia, Curvature lines of a transversal equiaffine vector field along a surface in 3-space, Journal of Singularities, v.25, 134-143, 2022.
- M.Craizer and S.Pesco, Centroaffine duality for spatial polygons, Discrete and Computational Geometry, v.19, 00136, 2019.
- F.Oliveira, A.Lins, A.Barreto, M.Craizer, H.Lopes, S.Pesco, Smoothing Tidal Effects in Well Test Pressure Data, IEEE Geoscience and Remote Sensing Letters, v.17, 899-902, 2019.
- R.S. dos Santos and M.Craizer, Isoperimetric Inequalities in Normed Planes, Journal of Convex Analysis, v.29, 321-331, 2022.
- M.Craizer and R.A.Garcia,
Singularities of Generic Line Congruences, Journal of the Mathematical
Society of Japan, 1-25, September 2022.
- Books and Course Notes
- M.Craizer and G.Tavares, Cálculo Integral de Várias Variáveis EDPUC, 2002 (in portuguese).
- M.Craizer and G.Tavares, Equações de Evolução em Processamento de Imagens, CNMAC2001 (in portuguese).
- M.Craizer, Equações de Evolução em Processamento de Imagens, Sibgrapi2001 (in portuguese). Revista de Informática Teórica e Aplicada, volume 8, número 2, 2001.
e-mail: craizer@puc-rio.br