mathematics

Ulrich Pinkall

Ulrich Pinkall is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Ulrich Pinkall rather than just read about it. In short: Ulrich Pinkall (born 1955) is a German mathematician, specializing in differential geometry and computer graphics. Pinkall studied mathematics at the University of Freiburg with a Diplom in 1979 and a doctorate in 1982 with thesis Dupin'sche Hyperflächen (Dupin's hypersurfaces) under the supervision of Martin Barner.

Key takeaways

Ulrich Pinkall belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Ulrich Pinkall to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Ulrich Pinkall from memory before moving on to harder problems.

Reference excerpt

Ulrich Pinkall (born 1955) is a German mathematician, specializing in differential geometry and computer graphics. Pinkall studied mathematics at the University of Freiburg with a Diplom in 1979 and a doctorate in 1982 with thesis Dupin'sche Hyperflächen (Dupin's hypersurfaces) under the supervision of Martin Barner. Pinkall was then a research assistant in Freiburg until 1984 and from 1984 to 1986 at the Max Planck Institute for Mathematics in Bonn. In 1985 he completed his habilitation in Bonn with thesis Totale Absolutkrümmung immersierter Flächen (Total absolute curvature of immersed surfaces). Since 1986 he is professor at TU Berlin. In 1985 he received the Otto Hahn Medal of the Max Planck Society. In 1986 he received a Heisenberg-Stipendium from the Deutsche Forschungsgemeinschaft (DFG). From 1992 to 2003 he was a speaker of the Sonderforschungsbereich (SFB) 288 (differential geometry and quantum physics). In 1998 he was an Invited Speaker with talk Quaternionic analysis of Riemann surfaces and differential geometry at the International Congress of Mathematicians in Berlin.

Selected publications Pinkall, U. (1985). "Regular homotopy classes of immersed surfaces" (PDF). Topology. 24 (4): 421–434. doi:10.1016/0040-9383(85)90013-8. Pinkall, U. (1985). "Hopf tori in S 3 {\displaystyle S^{3}} ". Inventiones Mathematicae. 81 (2): 379–386. Bibcode:1985InMat..81..379P. doi:10.1007/BF01389060. S2CID 120226082. Nomizu, Katsumi; Pinkall, Ulrich (1987). "On the geometry of affine immersions". Mathematische Zeitschrift. 195 (2): 165–178. doi:10.1007/BF01166455. S2CID 121027146. Kulkarni, Ravi S.; Pinkall, Ulrich, eds. (1988). Conformal geometry. Max-Planck-Institut für Mathematik, Seminar Bonn 1985/86. F. Vieweg. ISBN 978-3-528-08982-5. Karcher, H.; Pinkall, U.; Sterling, I. (1988). "New minimal surfaces in S 3 {\displaystyle S^{3}} ". Journal of Differential Geometry. 28 (2): 169–185. doi:10.4310/jdg/1214442276. 1988 Pinkall, U.; Sterling, I. (1989). "On the Classification of Constant Mean Curvature Tori". The Annals of Mathematics. 130 (2): 407. doi:10.2307/1971425. JSTOR 1971425. Burstall, F. E.; Ferus, D.; Pedit, F.; Pinkall, U. (1993). "Harmonic Tori in Symmetric Spaces and Commuting Hamiltonian Systems on Loop Algebras". The Annals of Mathematics. 138 (1): 173–212. doi:10.2307/2946637. JSTOR 2946637. Pinkall, Ulrich; Polthier, Konrad (1993). "Computing Discrete Minimal Surfaces and Their Conjugates". Experimental Mathematics. 2: 15–36. doi:10.1080/10586458.1993.10504266. Kulkarni, R. S.; Pinkall, U. (1994). "A canonical metric for Möbius structures and its applications". Mathematische Zeitschrift. 216 (1): 89–129. doi:10.1007/BF02572311. S2CID 116845289. Bobenko, A. I.; Pinkall, U. (1994). "Discrete surfaces with constant negative Gaussian curvature and the Hirota equation". (No. SFB-288-P-127) P00024647. "Discrete isothermic surfaces". Journal für die Reine und Angewandte Mathematik. 1996 (475): 187–208. 1996. doi:10.1515/crll.1996.475.187. S2CID 120432228. Bobenko, Alexander I.; Pinkall, Ulrich (1999). "Discretization of surfaces and integrable systems". In Bobenko, Alexander I.; Seiler, Ruedi (eds.). Discrete integrable geometry and physics. Oxford University Press. pp. 3–58. ISBN 9780198501602. Ferus, D.; Leschke, K.; Pedit, F.; Pinkall, U. (2001). "Quaternionic holomorphic geometry: Plücker formula, Dirac eigenvalue estimates and energy estimates of harmonic 2-tori". Inventiones Mathematicae. 146 (3): 507–593. arXiv:math/0012238. Bibcode:2001InMat.146..507F. doi:10.1007/s002220100173. S2CID 17979449. arXiv preprint Burstall, Francis E.; Ferus, Dirk; Leschke, Katrin; Pedit, Franz; Pinkall, Ulrich (2004-10-20). Conformal Geometry of Surfaces in S 4 {\displaystyle S^{4}} and Quaternions. Springer. ISBN 9783540453017. Springborn, Boris; Schröder, Peter; Pinkall, Ulrich (2008). "Conformal equivalence of triangle meshes". ACM Transactions on Graphics. 27 (3): 1. doi:10.1145/1360612.1360676. Chao, Isaac; Pinkall, Ulrich; Sanan, Patrick; Schröder, Peter (2010). "A simple geometric model for elastic deformations". ACM Transactions on Graphics. 29 (4): 1. doi:10.1145/1778765.1778775.

References

External links Ulrich Pinkall publications indexed by Google Scholar Official website

Worked examples

Example 1 — a first encounter with Ulrich Pinkall

Start with the simplest possible case. Write down what Ulrich Pinkall claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Ulrich Pinkall before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Ulrich Pinkall ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Ulrich Pinkall

In research: Ulrich Pinkall appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Ulrich Pinkall in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Ulrich Pinkall is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1955 births, 20th-century German mathematicians, 21st-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Ulrich Pinkall outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Ulrich Pinkall in 20 minutes

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Frequently asked questions

What is Ulrich Pinkall in simple terms?

Why does Ulrich Pinkall matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Ulrich Pinkall?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Ulrich Pinkall.