# Vasyl O. Gorkavyy

Doctor of sciences in physics and mathematics, docent (associate professor)

## List of selected publications

**Gorkavyy V.**
*One integral inequality for closed curve in Euclidean space* //
C. R. Acad. Sci., Paris, Ser. I,
v.321 (1995), №12, p.1587-1591,

Keywords: closed curve, curvature, Fary-Milnor inequality

**Gorkavyy V.**
*Reconstruction of a submanifold of Euclidean space from its Grassmannian image that degenerates into a line* //
Mathematical Notes,
V.59 (1996), №5, p. 490-497,

Keywords: Grassmann image, degenerate Grassmann image, asymptotic curve

**Gorkavyy V.**
*An analogue of the Grassmannian image for submanifolds of a sphere* //
Sbornik: Mathematics ,
V.187 (1996), №9, p.1283-1300,

**Gorkavyy V.**
*Reconstruction of three-dimensional submanifolds of Euclidean space with large codimension from its Grassmannian image* //
Mathematical Notes,
V.62 (1997), №5-6, p.581-585,

**Gorkavyy V.**
*Theorem of reduction in the problem of reconstruction of sub-manifolds in Euclidean space from a given Grassmannian image* //
Matematicheskaya Fizika, Analiz, Geometria,
V.4 (1997), №3, p.309-333,

**Gorkaviy V.**
*Deformations of surfaces F2 in E4 that preserve the Gauss image* //
Proceedings of the Conference "Geometry and Applications" dedicated to the seventieth birthday of V.A. Toponogov (Novosibirsk, Russia, March 13-17, 2000),
P.34-57,

**Gorkavyy V.**
*On pseudo-spherical congruencies in E4* //
Matematicheskaya Fizika, Analiz, Geometria,
V.10 (2003), №4, p.498-504,

**Gorkaviy V., Aminov Yu.A., Sviatovets A.V.**
*On the reconstruction of particular closed surface in E4 from a given closed Grassmann image* //
Matematicheskaya Fizika, Analiz, Geometria,
V.11 (2004), №1, p.3-24 ,

**Gorkavyy V.**
*Bianchi congruencies for two-dimensional surfaces in Е4* //
Sbornik: Mathematics,
V.196 (2005), №9-10, p.1473-1493,

**Gorkavyy V.**
*On pseudospherical surfaces in E4 with Grassmann image of prescribed type* //
Journal of mathematical physics, analysis, geometry,
V.2 (2006), №2, p.138-148,

**Gorkavyy V.**
*On conformal transformations of surfaces in Minkowski space with preservation of the Gauss image * //
Russian Math. (Iz. VUZ),
V.50 (2006), №7, p.11-21,

**Gorkavyy V.**
*On minimal lightlike surfaces in Minkowski space-time* //
Differential Geometry and its Applications,
V.26 (2008), №2, p.133-139,

**Gorkavyy V.**
*On pseudo-spherical congruencies in spaces of constant curvature* //
Annals on the National Academy of Sciences of Ukraine,
(2008), №6, p.13-18,

**Gorkavyy V.O. , Nevmerzhytska O.M.**
*Ruled surfaces as pseudo-spherical congruencies* //
Journal of mathematical physics, analysis, geometry ,
V.5 (2009), №4, p.359-374,

**Gorkavyy V.A., Milka A.D.**
*Volume increasing linear bendings of right polyhedra* //
Proceedings of Institute of mathematics of NAS of Ukraine,
V.6 (2009), №2, p.152-182,

**Gorkavyy V.A., Milka A.D., Soboleva A.N.**
*Volume increasing linear bendings of prisms* //
Рroc. Intern. Geom. Center dω,
V.2 (2010), №1, p.7-26,

**Gorkavyy V.**
*On inflating closed mylar shells* //
Comptes Rendus. Mecanique,
V.338 (2010), №12, p.656-662,

**Gorkavyy V., Nevmerzhytska O.**
*Аn analogue of the Bianchi transformation for two-dimensional surfaces in the space S3 x R1* //
Mathematical Notes,
V.89 (2011), №6, p.833-845,

**Gorkavyy V.A.**
*An Example of Bianchi Transformation in E4* //
Journal of mathematical physics, analysis, geometry,
V.8 (2012), p. 240–247,

**Gorkavyy V., Nevmerzhitska O.**
*Pseudo-spherical submanifolds with degenerate Bianchi transformation* //
Results in mathematics,
V. 60 (2011), №1, p.103-116,

**Gorkavyy V.**
*A generalisation of Bianchi-Baecklund transformation of pseudo-spherical surfaces* //
Itogi nauki i techniki. Seria "Sovremennaya mathematika i ee prilozheniya. Tematicheskie obzory",
V. 126 (2014), p. 191-218,