Manifold

Results named in Tau Ceti's TauCeti.Geometry.Manifold modules and in no roadmap's section, as Tau Ceti has them at commit ace60277.

The ambient disc theorem in a… to Green's second identity on a…

• The ambient disc theorem in a manifold
• Andreotti–Frankel theorem for proper holomorphic immersions
• The Bochner formula
• Brown's bicollaring theorem
• Brown's collaring theorem, for a compact domain
• Cartan's formula for the Levi form
• Cartan's magic formula
• The Christoffel formula of the first kind
• Closed normal disc theorem for a closed smooth submanifold
• The contracted Ricci identity for the gradient
• The disc theorem in a ball
• The disc theorem in a manifold
• The divergence theorem on a manifold without boundary
• Einstein's constancy theorem
• Euclidean disc theorem
• The Frobenius theorem in coordinates
• The Gauss formula
• Green's first identity on a manifold without boundary
• Green's formula for d*d
• Green's second identity on a manifold without boundary

Hadamard's identity in the… to Riemann's removable singularity…

• Hadamard's identity in the algebra of smooth functions
• Hadamard's lemma in coordinates
• The identity theorem on analytic manifolds
• The integrated Bochner identity
• The inverse function theorem for manifolds
• Jacobi's formula on a manifold
• The joint holomorphic implicit function theorem in charts
• The Koszul formula
• The Lichnerowicz estimate
• The local Frobenius theorem (TauCeti.IsInvolutiveDistribution.exists_flatChart)
• Milnor's cell attachment theorem
• Milnor's index bound on a smooth affine complete intersection
• Noncompact Euclidean tubular neighbourhood theorem
• The oriented common-centre disc theorem
• The Poincaré lemma on manifolds
• The Poincaré–Wirtinger inequality on a closed Riemannian manifold
• The regular-fibre theorem
• The relative ambient disc theorem
• The Ricci identity
• Riemann's removable singularity theorem on complex curves

Robbin–Salamon Corrigendum… to Weierstrass preparation theorem…

• Robbin–Salamon Corrigendum Lemma B (on arbitrary real normed spaces under C² regularity)
• Sard's theorem for smooth maps
• Schur's theorem (CovariantDerivative.eq_of_forall_hasSectionalCurvatureAt)
• Sharp local Lipschitz bound for the extended chart
• Smooth Euclidean tubular neighbourhood theorem
• Smooth Riemannian tubular neighbourhood theorem
• Smooth tubular neighbourhood theorem
• The Sobolev inequality near a point
• The straightening theorem [Lee, Thm. 9.22]
• The transverse fibre-product theorem
• Trudinger's inequality near a point
• Tubular neighbourhood theorem
• Weierstrass division theorem in holomorphic stalks
• Weierstrass preparation theorem in holomorphic stalks

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