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  • 1.
    Choe, Jaigyoung
    et al.
    Korea Inst Adv Study, Seoul 02455, South Korea..
    Hoppe, Jens
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Higher dimensional Schwarz's surfaces and Scherk's surfaces2018In: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 57, no 4, article id 107Article in journal (Refereed)
    Abstract [en]

    Higher dimensional generalizations of Schwarz's P-surface, Schwarz's D-surface and Scherk's second surface are constructed as complete embedded periodic minimal hypersurfaces in R-n.

  • 2.
    Hoppe, Jens
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Geodesics on ellipsoids2017Conference paper (Refereed)
    Abstract [en]

    Various ways of describing geodesic motion on Ellipsoids are presented (intrinsic and constrained formulations) including Jacobi’s solution, Weierstrass’ solution, and level set Liouville integrability.

  • 3.
    Hoppe, Jens
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Linardopoulos, Georgios
    Turgut, O. Teoman
    New minimal hypersurfaces in R(k+1)(2k+1) and S2k2+3k2017In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 290, no 17-18, p. 2874-2878Article in journal (Refereed)
    Abstract [en]

    We find a class of minimal hypersurfaces H-k as the zero level set of Pfaffians, resp. determinants of real 2k + 2 dimensional antisymmetric matrices. While H-1 and H-2 are congruent to the quadratic cone x(1)(2) + x(2)(2) + x(3)(2) - x(4)(2) - x(5)(2) - x(6)(2) = 0 resp. Hsiang's cubic su (4) invariant in R-15, H-k>2 (special harmonic SO (2k + 2)-invariant cones of degree >= 4) seem to be new.

  • 4.
    Hoppe, Jens
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Tkachev, Vladimir G.
    Linkoping Univ, Dept Math, Linkoping, Sweden..
    New construction techniques for minimal surfaces2019In: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 64, no 9, p. 1546-1563Article in journal (Refereed)
    Abstract [en]

    It is pointed out that despite the nonlinearity of the underlying equations, there do exist rather general methods that allow to generate new minimal surfaces from known ones.

  • 5. Markdahl, Johan
    et al.
    Hoppe, Jens
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Wang, Lin
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A geodesic feedback law to decouple the full and reduced attitude2017In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 102, p. 32-41Article in journal (Refereed)
    Abstract [en]

    This paper presents a novel approach to the problem of almost global attitude stabilization. The reduced attitude is steered along a geodesic path on the n - 1-sphere. Meanwhile, the full attitude is stabilized on SO(n). This action, essentially two maneuvers in sequel, is fused into one smooth motion. Our algorithm is useful in applications where stabilization of the reduced attitude takes precedence over stabilization of the full attitude. A two parameter feedback gain affords further trade-offs between the full and reduced attitude convergence speed. The closed loop kinematics on SO(3) are solved for the states as functions of time and the initial conditions, providing precise knowledge of the transient dynamics. The exact solutions also help us to characterize the asymptotic behavior of the system such as establishing the region of attraction by straightforward evaluation of limits. The geometric flavor of these ideas is illustrated by a numerical example.

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