science

Tom Ilmanen

Tom Ilmanen is a science 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 Tom Ilmanen rather than just read about it. In short: Tom Ilmanen (1961–2025) was an American mathematician specializing in differential geometry and the calculus of variations. He was a professor at ETH Zurich.

Key takeaways

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

Reference excerpt

Tom Ilmanen (1961–2025) was an American mathematician specializing in differential geometry and the calculus of variations. He was a professor at ETH Zurich. He obtained his PhD in 1991 at the University of California, Berkeley with Lawrence Craig Evans as supervisor. Ilmanen and Gerhard Huisken used inverse mean curvature flow to prove the Riemannian Penrose conjecture, which is the fifteenth problem in Yau's list of open problems, and was resolved at the same time in greater generality by Hubert Bray using alternative methods. In their 2001 paper, Huisken and Ilmanen made a conjecture on the mathematics of general relativity, about the curvature in spaces with very little mass: as the mass of the space shrinks to zero, the curvature of the space also shrinks to zero. This was proved in 2023 by Conghan Dong and Antoine Song. In an influential 1995 preprint, Ilmanen made the following conjecture:

For a smooth one-parameter family of closed embedded surfaces in Euclidean 3-space flowing by mean curvature, every tangent flow at the first singular time has multiplicity one. This has become known as the "multiplicity-one" conjecture. Richard Bamler and Bruce Kleiner proved the multiplicity-one conjecture in a 2023 preprint. Ilmanen received a Sloan Fellowship in 1996. He wrote the research monograph Elliptic Regularization and Partial Regularity for Motion by Mean Curvature.

Selected publications Huisken, Gerhard, and Tom Ilmanen. "The inverse mean curvature flow and the Riemannian Penrose inequality." Journal of Differential Geometry 59.3 (2001): 353–437. DOI: 10.4310/jdg/1090349447 Ilmanen, Tom. "Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature." Journal of Differential Geometry 38.2 (1993): 417–461. Feldman, Mikhail, Tom Ilmanen, and Dan Knopf. "Rotationally symmetric shrinking and expanding gradient Kähler-Ricci solitons." Journal of Differential Geometry 65.2 (2003): 169–209.

References

External links Nathalie Geiger (2026), "In memoriam Tom Ilmanen" ETH Zurich - Department of Mathematics - News & Events

Worked examples

Example 1 — a first encounter with Tom Ilmanen

Start with the simplest possible case. Write down what Tom Ilmanen claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 Tom Ilmanen 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 Tom Ilmanen 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 Tom Ilmanen

In research: Tom Ilmanen appears in science 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 Tom Ilmanen 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: Tom Ilmanen is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1961 births, Academic staff of ETH Zurich, Differential geometers, so understanding it makes those chapters shorter.
In everyday life: Look for Tom Ilmanen 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 Tom Ilmanen in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Tom Ilmanen 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 Tom Ilmanen out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Tom Ilmanen in simple terms?

Tom Ilmanen (1961–2025) was an American mathematician specializing in differential geometry and the calculus of variations. He was a professor at ETH Zurich.

Why does Tom Ilmanen matter?

Because it connects several science 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 Tom Ilmanen?

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 Tom Ilmanen.