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Hoppe, Jens
Publications (5 of 5) Show all publications
Hoppe, J. & Tkachev, V. G. (2019). New construction techniques for minimal surfaces. Complex Variables and Elliptic Equations, 64(9), 1546-1563
Open this publication in new window or tab >>New construction techniques for minimal surfaces
2019 (English)In: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 64, no 9, p. 1546-1563Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
TAYLOR & FRANCIS LTD, 2019
Keywords
Dmitry Khavinson, Minimal surfaces, entire solutions, perfectly harmonic functions, Backlund transformation
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-255397 (URN)10.1080/17476933.2018.1542688 (DOI)000473635700007 ()2-s2.0-85057345720 (Scopus ID)
Note

QC 20190814

Available from: 2019-08-14 Created: 2019-08-14 Last updated: 2019-08-27Bibliographically approved
Choe, J. & Hoppe, J. (2018). Higher dimensional Schwarz's surfaces and Scherk's surfaces. Calculus of Variations and Partial Differential Equations, 57(4), Article ID 107.
Open this publication in new window or tab >>Higher dimensional Schwarz's surfaces and Scherk's surfaces
2018 (English)In: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 57, no 4, article id 107Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Springer, 2018
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-240206 (URN)10.1007/s00526-018-1372-4 (DOI)000436012500001 ()2-s2.0-85049321134 (Scopus ID)
Note

QC 20181217

Available from: 2018-12-17 Created: 2018-12-17 Last updated: 2019-05-02Bibliographically approved
Markdahl, J., Hoppe, J., Wang, L. & Hu, X. (2017). A geodesic feedback law to decouple the full and reduced attitude. Systems & control letters (Print), 102, 32-41
Open this publication in new window or tab >>A geodesic feedback law to decouple the full and reduced attitude
2017 (English)In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 102, p. 32-41Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Elsevier, 2017
Keywords
Attitude control, Reduced attitude, Geodesics, Exact solutions, Special orthogonal group
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-207709 (URN)10.1016/j.sysconle.2017.01.005 (DOI)000399862600005 ()2-s2.0-85012131906 (Scopus ID)
Funder
Swedish Foundation for Strategic Research Swedish Research Council
Note

QC 20170524

Available from: 2017-05-24 Created: 2017-05-24 Last updated: 2017-11-10Bibliographically approved
Hoppe, J. (2017). Geodesics on ellipsoids. In: : (pp. 229-238). Springer International Publishing (9783319524696)
Open this publication in new window or tab >>Geodesics on ellipsoids
2017 (English)Conference paper, Published 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.

Place, publisher, year, edition, pages
Springer International Publishing, 2017
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-216577 (URN)10.1007/978-3-319-52471-9_15 (DOI)2-s2.0-85029183325 (Scopus ID)
Note

QC 20171101

Available from: 2017-11-01 Created: 2017-11-01 Last updated: 2017-11-01Bibliographically approved
Hoppe, J., Linardopoulos, G. & Turgut, O. T. (2017). New minimal hypersurfaces in R(k+1)(2k+1) and S2k2+3k. Mathematische Nachrichten, 290(17-18), 2874-2878
Open this publication in new window or tab >>New minimal hypersurfaces in R(k+1)(2k+1) and S2k2+3k
2017 (English)In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 290, no 17-18, p. 2874-2878Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
WILEY-V C H VERLAG GMBH, 2017
Keywords
Differential Geometry, Minimal Hypersurfaces
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-221873 (URN)10.1002/mana.201600401 (DOI)000419959100013 ()
Note

QC 20180130

Available from: 2018-01-30 Created: 2018-01-30 Last updated: 2018-01-30Bibliographically approved
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