Ionin–Pestov theorem is not very well known, but it deserves to be included in standard introductory texts on differential geometry of curves. It gives the simplest meaningful example of a local-to-global theorem which is what differential geometry is about.

Theorem. Assume that a plane region $F$ is bounded by a simple loop with curvature at most $1$. Then $F$ contains a unit disc.

The original reference:

• Пестов, Г. Г., Ионин В. К. О наибольшем круге, вложенном в замкнутую кривую // Доклады АН СССР. — 1959. — Т. 127, № 6.

We used it in our textbook What is differential geometry.

Ionin–Pestov theorem is not very well known, but it deserves to be included in standard introductory texts on differential geometry of curves. It gives the simplest meaningful example of a local-to-global theorem which is what differential geometry is about.

Theorem. Assume that a plane region $F$ is bounded by a simple loop with curvature at most $1$. Then $F$ contains a unit disc.

The original reference:

• Пестов, Г. Г., Ионин В. К. О наибольшем круге, вложенном в замкнутую кривую // Доклады АН СССР. — 1959. — Т. 127, № 6.

We used it in our textbook What is differential geometry.

Ionin–Pestov theorem is not very well known, but it deserves to be included in standard introductory texts on differential geometry of curves. It gives the simplest meaningful example of a local-to-global theorem which what differential geometry is about.

Theorem. Assume that a plane region $F$ is bounded by a simple loop with curvature at most $1$. Then $F$ contains a unit disc.

The original reference:

• Пестов, Г. Г., Ионин В. К. О наибольшем круге, вложенном в замкнутую кривую // Доклады АН СССР. — 1959. — Т. 127, № 6.

We used it in our textbook What is differential geometry.

Ionin–Pestov theorem is not very well known, but it deserves to be included in standard introductory texts on differential geometry of curves. It gives the simplest meaningful example of a local-to-global theorem which is what differential geometry is about.

Theorem. Assume that a plane region $F$ is bounded by a simple loop with curvature at most $1$. Then $F$ contains a unit disc.

The original reference:

• Пестов, Г. Г., Ионин В. К. О наибольшем круге, вложенном в замкнутую кривую // Доклады АН СССР. — 1959. — Т. 127, № 6.

We used it in our textbook What is differential geometry.