Category
page 1Theorems in differential geometry
Atiyah–Singer index theorem
theorem that the difference between the dimensions of the kernel and cokernel of a differential operator on a manifold is the integral of a characteristic class
Theorema Egregium
"Remarkable theorem" about Gauss' curvature as an invariant
Gauss–Bonnet theorem
Theorem in differential geometry
Sard's theorem
theorem that the set of the critical values of a smooth function has measure zero
generalized Stokes' theorem
statement about integration of differential forms on manifolds
Darboux's theorem
foundational result in symplectic geometry
four-vertex theorem
theorem that every simple closed smooth curve in the plane has at least four points of locally extreme curvature
Generalized Gauss-Bonnet theorem
uniformization theorem
theorem that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere
Euler's theorem
theorem in the mathematical field of differential geometry
Frobenius theorem
theorem that a distribution is integrable iff it arises from a regular foliation
Meusnier's theorem
theorem in differential geometry
Bernstein's problem
problem in differential geometry
Mostow rigidity theorem
Theorem in hyperbolic geometry
Hilbert's theorem
Tennis ball theorem
smooth curve that divides a sphere into 2 equal-area subsets has at least 4 inflections
theorem of the three geodesics
theorem that every Riemannian manifold with the topology of a sphere has at least 3 closed geodesics
fundamental theorem of curves
theorem
prime decomposition of a 3-manifold
Decomposes compact, orientable 3-manifolds uniquely into finitely many prime 3-manifolds