30 Answers votes newest views recent 1Differential of a Sobolev map between manifolds 2Elliptic pseudodifferential operator estimate -2Yang Mills gradient/heat flow on 4-torus 0norm of n-th covariant derivative of smooth function 3Eqivalency of two norms on the symmetric two tensor-fields on a compact Riemannian manifold. 2Dimension of moduli space in Lagrangian Floer homology 3Are infinite dimensional constructions needed to prove finite dimensional results? (2) 18Proofs that require fundamentally new ways of thinking 1the slice theorem in the symplectic manifold 6existence of Morse functions satisfying the Palais-Smale condition 1What does “kernel” mean in integral kernel? 2Motivating the de Rham theorem 1Can the adjoint of the exterior derivative in semi-Riemannian geometry be defined without the Hodge * operator? 0Is the metric obtained by altering the metric of a Hilbert space on a finite-dimensional subspace equivalent to the original one? 2Singular, holonomy-free connections on Riemannian surfaces? 3What is torsion in differential geometry intuitively? 1Clifford Algebra in Dirac Equation 0Difference between measures and distributions 3Why is cotangent more canonical than tangent? 2How to see the Phase Space of a Physical System as the Cotangent Bundle 0Are the strata of Nakajima quiver varieties simply-connected? Do they have odd cohomology? 10How much of differential geometry can be developed entirely without atlases? 4What do heat kernels have to do with the Riemann-Roch theorem and the Gauss-Bonnet theorem? 6PDE on manifolds 3Understanding moment maps and lie brackets 2What’s algebraic approach to QM good for? 3Is there a good (co)homology theory for manifolds with corners? 6Is there a Morse theory for sections of bundles or more generally for maps? 12Stokes theorem for manifolds with corners? 2Gauge connections and Lie algebras?