Publications
Spectrum of the Laplacian and the Jacobi Operator on Generalized Rotational Minimal Hypersurfaces of Spheres
Differential Geometry: We introduce a natural extension of the classical notion of surfaces of revolution (or rotational hypersurfaces), which yields a new family of minimal and constant mean curvature hypersurfaces in the sphere
Intuitive Real-Time Robot Teleoperation via VR, ROS, and Externally Guided Motion for Human Skill Transfer
Robotics: We integrated virtual reality (VR) and robotic teleoperation through a user-friendly motion capture control system, aiming to broaden the accessibility of teleoperated robotic systems for heavily labor and skill intensive manufacturing processes, such as airfoil deburring and blending
Cmc hypersurfaces with two principal curvatures
Differential Geometry: We describe all cmc hypersurfaces with two principal curvatures in all space forms. This classification includes the ambient spaces: Spheres, Euclidean spaces, Hyperbolic spaces, de-Sitter spaces, anti de Sitter spaces and Minkowski spaces
Preparation of three-qubits states
Quantum Information: We describe a very concise method to prepare any 3-qubit state using the minimum number of non-local gates. We also consider the case where all the amplitudes of the 3-qubit state are real.
Reconstructing Euler's work on collinear solutions of the 3-body problem and identifying their corresponding Lagrange points
Celestial Mechanics: Euler described all posible solutions of the 3-body problem where the three bodies are on the same line. In this paper the author provides a different proof of this characterization and for each solution, he finds its Lagrange points. This is, the author find all circular solutions (with the same angular velocity as the primaries) of the restricted 4-body problem.
Periodic oscillations in the 2N-body problem
Celestial Mechanics: We find periodic soltuion of the 2N body problem.
Periodic oscillations in the restricted hip-hop 2N+1-body problem
Celestial Mechanics: We find periodic soltuion of the restricted (2N+1)-body problem.
Bifurcation of periodic orbits for the N-body problem, from a non geometrical family of solutions
Celestial Mechanics: We find periodic soltuions of the restricted N-body problem.
Four qubits generated by Clifford gates
Quantum Information: We describe the connectivity of all 4-qubit stabilisers
Robust implementation of generative modeling with parametrized quantum circuits
Quantum Information: A black box solver is described and compared
Entanglement types for two-qubit states with real amplitudes
Quantum Information: A geometric interpretation for the entropy of two qubit is shown.
Canonical representation of three-qubit states with real amplitudes
Quantum Information: Using differential geometric techniques, we find a canonical representation of three-qubit states with real amplitudes
Constant-speed ramps for a central force field
Differential Geometry and physics: We characterize all possible ways of ramps where objects will fall with constant speed under the assumption that there are under a central force field
Spectrum of the Laplacian and the Jacobi operator on rotational CMC hypersurfaces of spheres.
Differential Geometry : We compute the eigenvalues of the Laplacian and the stability operator defined on rotational CMC hypersurfaces
Clifford 3-qubit states.
Quantum Information : We explain the connectivity of 3-qubit stabilisers.
The round Taylor method.
Numerical Analysis : I developed a numerical method that considers round-off error.
Algebraic CMC hypersurfaces of order 3 in Euclidean spaces
Differential Geometry : We characterize all algebrac CMC hypersursurfaces defined by a polynomial of order 3 in the Euclidean space.
A generative modeling approach for benchmarking and training shallow quantum circuit
Quantum information : I helped in this paper computing entropies and using a black box solver (created by myself) to find states minimize the entropy.
Training of Quantum Circuits on a Hybrid Quantum Computer
Quantum information : I helped in this paper computing entropies and using a black box solver (created by myself) to find states minimize the entropy.
On the stability of periodic solution with defined sign in MEMS via lower and upper solutions
Dynamical systems : I helped in this paper by doing a continuation method that generated a family of periodic solutions
A Bifurcation in the Family of Periodic Orbits for the Spatial Isosceles 3 Body Problem
Celestial Mechanics : I generated a family of periodic solutions of the 3-body problem.
Minimal translational surfaces in Euclidean space.
Differential Geometry : We discribe all minimal tranlational surfaces in ℝ3
On the period of the periodic orbits of the restricted three body problem.
Celestial Mechanics : There are 5 Lagrange points. Near the Lagrange points L4 and L5, it is likely to have a zero-mass body rotating about these points. We show that if one of these bodies is rotating around L4, then the rotation of this body must be clockwise.
On the flapping motion of a helicopter blade.
Helicopoter Theory : We describe peridos solutions for the flapping motion of the helicopter blade
Equilibrium shapes of cylindrical rotating drops
Differential Geometry : We describe the shape of drop when there is not gravitional force.
n-dimensional area of minimal rotational hypersurfaces in spheres.
Differential Geometry : We show the the possible areas of the minimal rotational hypesurfaces of sphers is discrete and study these areas.
A characterization of quadric constant Gauss-Kronecker curvature hypersurfaces of spheres
Area: Differential Geometry :
Constant speed ramps
Area: Differential Geometry and Engineering :
Rotating drops with helicoidal symmetry.
Area: Differential Geometry :
A characterization of quadric constant scalar curvature hypersurfaces of spheres.
Area: Differential Geometry :
Helicoidal minimal surfaces in ℝ3.
Area: Differential Geometry :
Algebraic constant mean curvature surfaces in Euclidean space.
Area: Differential Geometry :
Stability index jump for constant mean curvature hypersurfaces of spheres.
Area: Differential Geometry :
A dynamical interpretation of the profile curve of cmc Twizzlers surfaces.
Area: Differential Geometry :
CMC hypersurfaces on riemannian and semi-riemannian manifolds.
Area: Differential Geometry :
Algebraic zero mean curvature varieties in semi-riemannian manifolds.
Area: Differential Geometry :
Minimal tori with low nullity.
Area: Differential Geometry :
Embedded cmc hypersurfaces on hyperbolic spaces.
Area: Differential Geometry :
Superficies con curvatura media constante.
Area: Differential Geometry :
Embedded constant mean curvature hypersurfaces on spheres.
Area: Differential Geometry :
New examples of maximal space like surfaces in the anti-de Sitter space.
Area: Differential Geometry :
Rotational surfaces in S^3 with constant mean curvature
A characterization of quadratic constant mean curvature hypersurfaces of spheres
Characterization of order-3 algebraic immersed minimal surfaces of S^3
Metrics on products of surfaces with non-positive sectional curvature
Stable constant mean curvature hypersurfaces in the real projective space
On the stability index of hypersurfaces with constant mean curvature in spheres
Hipervariedades mínimas algebraicas en S^n
Authors: Mesa, H.; Perdomo, O. Journal: Revista de la Unión Matemática Argentina (2006).Non-existence of regular algebraic surfaces of spheres of degree 3
Morse theory for semianalytic functions
Distribution of minimal varieties in spheres in terms of the coordinate functions
On the average of the scalar curvature for minimal hypersurfaces of spheres with low index
Rigidity of minimal hypersurfaces with two principal curvatures
First eigenvalue characterization of Clifford hypersurfaces
Low index minimal hypersurfaces of spheres
Sobre el nacimiento de la geometría riemanniana
Author: Oscar Perdomo, Journal: Revista Tumbaga (2008).History of Mathematics: TBA
Métricas planas y el teorema de uniformización en toros mínimos de la esfera unidad 3-dimensional
Authors: Montaño, J.; Perdomo, O.; Salas, H. Journal: Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales (2008).Differential Geometry: TBA
Minimal torus invariant under one reflection
Author: Oscar Perdomo, Journal: Matemáticas: Enseñanza Universitaria (2007).Differential Geometry: TBA
Minimal hypersurfaces in ℝⁿ as regular values of a function
Author: Oscar Perdomo, Journal: Revista Integración – Temas de Matemáticas (2004).Differential Geometry: TBA
Nonembeddability of the Klein Bottle in RP³ and Lawson’s Conjecture
Author: Oscar Perdomo, Journal: Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales (2005).Differential Geometry: TBA
Another proof for the rigidity of Clifford minimal hypersurfaces of Sⁿ
Author: Oscar Perdomo, Journal: Matemáticas: Enseñanza Universitaria (2005).Differential Geometry: TBA
Rigidity of minimal hypersurfaces of spheres with constant Ricci curvature
Author: Oscar Perdomo, Journal: Revista Colombiana de Matemáticas (2004).Differential Geometry: TBA
Mathematical foundations of a surface made out of triangles
Author: Oscar Perdomo, Journal: Revista Epiciclos (2005).Differential Geometry: TBA
Gráficas de funciones sobre variedades
Author: Oscar Perdomo, Journal: Matemáticas: Enseñanza Universitaria (2004).Differential Geometry: TBA
Stable minimal hypersurfaces in ℝ⁸ and ℝ⁹ with constant scalar curvature
Author: Oscar Perdomo, Journal: Revista Colombiana de Matemáticas (2002).Differential Geometry: TBA
Totally geodesic surfaces and Hopf’s conjecture
Author: Oscar Perdomo, Journal: Matemáticas: Enseñanza Universitaria (2002).Differential Geometry: TBA
La aplicación de Gauss de una superficie mínima completa y lagrangiana no puede omitir más de 4 puntos
Author: Oscar Perdomo, Journal: Memorias III Escuela de Verano, Universidad de los Andes (1995).Differential Geometry: TBA