PIGTIKAL (puzzles in geometry that I know and love)
Anton Petrunin
TL;DR
PIGTIKAL collects graduate-level geometry puzzles across curves, surfaces, comparison geometry, curvature-free geometry, and metric geometry, each with concise solutions intended to sharpen problem-solving skills. It showcases a repertoire of techniques—such as nested osculating circles for curvature control, convexity and Gauss-type comparisons on surfaces, Liouville and Kirszbraun-type extension arguments, Besicovitch inequalities, and GH-type approximations—to derive sharp, elegant conclusions. The volume includes semisolutions and cross-cutting insights that tie together classical results (e.g., Gauss–Bonnet, Coxeter-type arguments) with modern metric-geometry ideas, illustrating both foundational theorems and novel constructions. Overall, the book aims to equip readers with compact, technique-driven reasoning that transfers across differential, metric, and geometric contexts, enhancing both theoretical understanding and problem-solving agility.
Abstract
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 when the problem was discovered.