mathematics

Henry C. Wente

Henry C. Wente 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 Henry C. Wente rather than just read about it. In short: Henry Christian Wente (August 18, 1936 – January 20, 2020) was an American mathematician, known for his 1997 discovery of the Wente torus, an immersed constant-mean-curvature surface whose existence disproved a conjecture of Heinz Hopf. Wente obtained both his bachelor's degree and his Ph.D. from Harvard University.

Key takeaways

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

Reference excerpt

Henry Christian Wente (August 18, 1936 – January 20, 2020) was an American mathematician, known for his 1997 discovery of the Wente torus, an immersed constant-mean-curvature surface whose existence disproved a conjecture of Heinz Hopf. Wente obtained both his bachelor's degree and his Ph.D. from Harvard University. He completed his doctorate in 1966, under the supervision of Garrett Birkhoff. He was a distinguished professor emeritus of mathematics at the University of Toledo, which he joined in 1971. In 1988 he was an Invited Speaker at the International Congress of Mathematicians (ICM) in Berkeley, California. In 2012 he became a fellow of the American Mathematical Society.

Selected publications

Articles —— (1971). "An existence theorem for surfaces of constant mean curvature". Bulletin of the American Mathematical Society. 77 (2): 200–203. doi:10.1090/S0002-9904-1971-12679-4. MR 0268743. —— (1971). "A general existence theorem for surfaces of constant mean curvature". Mathematische Zeitschrift. 120 (3): 277–288. doi:10.1007/BF01117500. Hildebrandt, S.; —— (1973). "Variational problems with obstacles and a volume constraint". Mathematische Zeitschrift. 135: 55–68. doi:10.1007/BF01214305. —— (1974). "The Dirichlet problem with a volume constraint". Manuscripta Mathematica. 11 (2): 141–157. doi:10.1007/BF01184954. —— (1975). "The differential equation Δ {\displaystyle \Delta } x=2H(xu ∧ {\displaystyle \wedge } xv) with vanishing boundary values". Proceedings of the American Mathematical Society. 50 (1): 131–137. doi:10.2307/2040528. JSTOR 2040528. MR 0374673. Steffen, Klaus; —— (1978). "The non-existence of branch points in solutions to certain classes of plateau type variational problems". Mathematische Zeitschrift. 163 (3): 211–238. doi:10.1007/BF01174896. —— (1980). "Large solutions to the volume constrained plateau problem". Archive for Rational Mechanics and Analysis. 75 (1): 59–77. Bibcode:1980ArRMA..75...59W. doi:10.1007/BF00284621. —— (1982). "The symmetry of rotating fluid bodies". Manuscripta Mathematica. 39 (2–3): 287–296. doi:10.1007/BF01165793. —— (1985). "A counterexample in 3-space to a conjecture of H. Hopf". Arbeitstagung Bonn 1984. Lecture Notes in Mathematics. Vol. 1111. pp. 421–429. doi:10.1007/BFb0084601. ISBN 978-3-540-15195-1. —— (1987). "Immersed Tori of Constant Mean Curvature in R 3 {\displaystyle \mathbb {R} ^{3}} ". Variational Methods for Free Surface Interfaces. pp. 13–26. doi:10.1007/978-1-4612-4656-5_2. ISBN 978-1-4612-9101-5. —— (1987). "Twisted Tori of Constant Mean Curvature in R 3 {\displaystyle \mathbb {R} ^{3}} ". Seminar on New Results in Nonlinear Partial Differential Equations. pp. 1–36. doi:10.1007/978-3-322-85049-2_1. ISBN 978-3-322-85051-5. Sterling, I.; —— (1993). "Existence and Classification of Constant Mean Curvature Multibubbletons of Finite and Infinite Type". Indiana University Mathematics Journal. 42 (4): 1239–1266. doi:10.1512/iumj.1993.42.42057. JSTOR 24897145. —— (1995). "The capillary problem for an infinite trough". Calculus of Variations and Partial Differential Equations. 3 (2): 155–192. doi:10.1007/BF01205004. —— (1999). "A surprising bubble catastrophe". Pacific Journal of Mathematics. 189 (2): 339–375. doi:10.2140/pjm.1999.189.339. —— (2002). "Constant mean curvature surfaces of annular type". Calculus of Variations and Partial Differential Equations. 14 (2): 193–211. doi:10.1007/s005260100097. —— (2008). "The Floating Ball Paradox". Journal of Mathematical Fluid Mechanics. 10 (4): 569–582. Bibcode:2008JMFM...10..569W. doi:10.1007/s00021-007-0251-0. —— (2011). "Exotic Capillary Tubes". Journal of Mathematical Fluid Mechanics. 13 (3): 355–370. Bibcode:2011JMFM...13..355W. doi:10.1007/s00021-010-0027-9.

Books —— (1992). Constant Mean Curvature Immersions of Enneper Type. American Mathematical Soc. ISBN 978-0-8218-2536-5.

References

Worked examples

Example 1 — a first encounter with Henry C. Wente

Start with the simplest possible case. Write down what Henry C. Wente 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 Henry C. Wente 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 Henry C. Wente 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 Henry C. Wente

In research: Henry C. Wente 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 Henry C. Wente 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: Henry C. Wente is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1936 births, 2020 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Henry C. Wente 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 Henry C. Wente in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Henry C. Wente means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Henry C. Wente out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Henry C. Wente in simple terms?

Why does Henry C. Wente 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 Henry C. Wente?

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 Henry C. Wente.