MSC2020 · 51-XX

Geometry

Geometry \{For algebraic geometry, see 14-XX; for differential geometry, see 53-XX\}

15 mapped entries · Browse and filter all →

Counts include all statuses and descendants. Classifications are editorial or inferred from community fields, not an AMS assessment of the problem.

Subcategories

51-00General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to geometry0 51-01Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry0 51-02Research exposition (monographs, survey articles) pertaining to geometry0 51-03History of geometry0 51-04Software, source code, etc. for problems pertaining to geometry0 51-06Proceedings, conferences, collections, etc. pertaining to geometry0 51-08Computational methods for problems pertaining to geometry0 51-11Research data for problems pertaining to geometry0 51AxxLinear incidence geometry0 51BxxNonlinear incidence geometry0 51CxxRing geometry (Hjelmslev, Barbilian, etc.)0 51DxxGeometric closure systems0 51ExxFinite geometry and special incidence structures0 51FxxMetric geometry15 51GxxOrdered geometries (ordered incidence structures, etc.)0 51HxxTopological geometry0 51JxxIncidence groups0 51KxxDistance geometry0 51LxxGeometric order structures0 51MxxReal and complex geometry0 51NxxAnalytic and descriptive geometry0 51PxxClassical or axiomatic geometry and physics0

Mapped problems

OP-11894Geometry and topologyStatus unassessed

Guth’s sponge embedding problem

Guth’s sponge embedding problem. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

Anton Petrunin — A Gallery of Geometry Problems· Source question · editorial summary· 2026

OP-11893Geometry and topologyStatus unassessed

Smooth optical fibers: orthogonal slices and noncongruent ends

Smooth optical fibers: orthogonal slices and noncongruent ends. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

Anton Petrunin — A Gallery of Geometry Problems· Source question · editorial summary· 2026

OP-11892Geometry and topologyStatus unassessed

Reconstructing a pointed manifold from its exponential pullback

Reconstructing a pointed manifold from its exponential pullback. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

Anton Petrunin — A Gallery of Geometry Problems· Source question · editorial summary· 2026

OP-11891Geometry and topologyStatus unassessed

Almost every geodesic encounters negative curvature

Almost every geodesic encounters negative curvature. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

Anton Petrunin — A Gallery of Geometry Problems· Source question · editorial summary· 2026

OP-11890Geometry and topologyStatus unassessed

Embedding a closed four-ball with open projection

Embedding a closed four-ball with open projection. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

Anton Petrunin — A Gallery of Geometry Problems· Source question · editorial summary· 2026

OP-11889Geometry and topologyStatus unassessed

Compactness of convex hulls in complete CAT(0) spaces

Compactness of convex hulls in complete CAT(0) spaces. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

Anton Petrunin — A Gallery of Geometry Problems· Source question · editorial summary· 2026

OP-11888Geometry and topologyStatus unassessed

Cocompact hyperbolic actions generated by finite-order elements

Cocompact hyperbolic actions generated by finite-order elements. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

Anton Petrunin — A Gallery of Geometry Problems· Source question · editorial summary· 2026

OP-11887Geometry and topologyStatus unassessed

Nonnegative polyhedral approximation of complex projective space

Nonnegative polyhedral approximation of complex projective space. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

Anton Petrunin — A Gallery of Geometry Problems· Source question · editorial summary· 2026

OP-11886Geometry and topologyStatus unassessed

Length of a geodesic fixed by an involution

Length of a geodesic fixed by an involution. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

Anton Petrunin — A Gallery of Geometry Problems· Source question · editorial summary· 2026

OP-11885Geometry and topologyStatus unassessed

Connecting points of a compact continuum with little outside length

Connecting points of a compact continuum with little outside length. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

Anton Petrunin — A Gallery of Geometry Problems· Source question · editorial summary· 2026

Journals & articles in MSC 51

These are selected sources for the parent class. Article coverage is a first reviewed selection, and may not cover this exact subcategory.

Geometry & Topology ↗

Mathematical Sciences Publishers

Geometry and topology

Journal discovery is available; article-level extraction for this class is not yet included in this batch.

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