alexandrov spaces 1curvature bounded below 1globalization theorem 1gradient flows 1metric geometry 1splitting theorem 1
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math.HO2025
What is differential geometry: curves and surfaces
Anton Petrunin, Sergio Zamora Barrera
These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- t…
math.HO2025
Euclidean plane and its relatives; a minimalist introduction
Anton Petrunin
The book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalist. List of topics: Euclidean geometry: Th…
math.HO2025
PIGTIKAL (puzzles in geometry that I know and love)
Anton Petrunin
Problems for the graduate students who want to improve problem-solving skills in geometry. Every problem has a short elegant solution -- this gives a hint which was not available w…