Anton Petrunin — A Gallery of Geometry Problems
All 18 numbered topics in version 2 indexed. Three postscripts report solutions (9, 11, 13); these are excluded from the new problem records. Optical-fiber subquestions remain grouped.
18 catalogue entries · 15 new problem records · 15 catalogue entries linked to problem records
Catalogue entries can be source pointers, solved items or groups of questions. They are not added to the main problem count. Status reflects the saved source, inspected 2026-09-10.
Original collection ↗Attribution and reuse
CC0 1.0. Anton Petrunin; independent summaries of version 2, 7 September 2026.
18 matching entries
Clear filtersTwo-convexity and plane sections
Status unassessedGeometry gallery · PDF page 1
Editorial summary of the numbered source topic.
CAT(0) geometry of braid space
Status unassessedGeometry gallery · PDF page 2
Editorial summary of the numbered source topic.
Hilbert-space quotients and Riemannian biquotients
Status unassessedGeometry gallery · PDF page 3
Editorial summary of the numbered source topic.
Metrics of nested convex surfaces
Status unassessedGeometry gallery · PDF page 4
Editorial summary of the numbered source topic.
Maximal finite subgroups of Euclidean isometry groups
Status unassessedGeometry gallery · PDF page 4
Editorial summary of the numbered source topic.
Connecting points of a compact continuum with little outside length
Status unassessedGeometry gallery · PDF page 5
Editorial summary of the numbered source topic.
Length of a geodesic fixed by an involution
Status unassessedGeometry gallery · PDF page 6
Editorial summary of the numbered source topic.
Nonnegative polyhedral approximation of complex projective space
Status unassessedGeometry gallery · PDF page 6
Editorial summary of the numbered source topic.
Octahedron comparison — source reports a solution
Source marks solvedGeometry gallery · PDF page 7
Version 2 postscript reports a solution; not added as an open problem.
Cocompact hyperbolic actions generated by finite-order elements
Status unassessedGeometry gallery · PDF page 7
Editorial summary of the numbered source topic.
Milnor’s cartography problem — source reports a solution
Source marks solvedGeometry gallery · PDF page 8
Version 2 postscript reports a solution; not added as an open problem.
Compactness of convex hulls in complete CAT(0) spaces
Status unassessedGeometry gallery · PDF page 8
Editorial summary of the numbered source topic.
Disc norm on torus homeomorphisms — source reports a solution
Source marks solvedGeometry gallery · PDF page 9
Version 2 postscript reports a solution; not added as an open problem.
Embedding a closed four-ball with open projection
Status unassessedGeometry gallery · PDF page 9
Editorial summary of the numbered source topic.
Almost every geodesic encounters negative curvature
Status unassessedGeometry gallery · PDF page 9
Editorial summary of the numbered source topic.
Reconstructing a pointed manifold from its exponential pullback
Status unassessedGeometry gallery · PDF page 10
Editorial summary of the numbered source topic.
Smooth optical fibers: orthogonal slices and noncongruent ends
Status unassessedGeometry gallery · PDF page 10
Editorial summary of the numbered source topic.
Guth’s sponge embedding problem
Status unassessedGeometry gallery · PDF page 11
Editorial summary of the numbered source topic.