Reputation
13,746
Next privilege 15,000 Rep.
Protect questions
 Feb 3 comment Lipschitz Functions @user119459: The OP says specifically: "Assume that the sequence of functions has a common Lipschitz constant $K$." Jan 28 comment Geometric interpretation of connection forms, torsion forms, curvature forms, etc What does it mean (precisely) for two points $x,y \in M$ to be "infinitesimally close" or "close to first order"? Jan 27 comment $C^{\infty}_{C}(\Omega)$ it is dense in $W^{1,2}(\Omega)=H^1(\Omega)$ ? I know that it is dense in $H^1_{0}(\Omega).$ @MaoWao: That's a useful fact, thanks. Do you have a reference? Jan 18 awarded Good Answer Dec 22 awarded Popular Question Dec 19 awarded Good Question Dec 18 awarded Nice Question Dec 18 comment Why do we care about two subgroups being conjugate? @goblin: not necessarily. To endow $G/H_1$ and $G/H_2$ with group structures, then yes, I should have added normality in that line; I was being careless. Dec 18 comment Why do we care about differential forms? (Confused over construction) "... why write this as $dx$, which had previously been used to mean an infinitesimal increase in $x$." What exactly, precisely, is meant by an "infinitesimal" increase in $x$? Unless one goes the (somewhat cumbersome) route of "non-standard analysis," there isn't a precise meaning of this -- until one introduces differential forms. Dec 18 asked Why do we care about two subgroups being conjugate? Dec 18 reviewed Approve In what sense is this action of $\mathbb R$ on $T$ lifted to an action of $\pi_1(T)\times\mathbb R$ on $\mathbb R^2$? Dec 15 comment Is the supremum of the closure equal to the supremum of the set? What do you mean by "$\sup(M) \in \overline{M}$ in general"? Is $\text{sup}(M)$ a real number or an element of $X$? What is the definition of $\sup(M)$? Dec 15 revised How to prove $d\omega=(\nabla_\mu\omega)_\nu dx^\mu\wedge dx^\nu$ without using coordinates edited body Dec 14 answered How to prove $d\omega=(\nabla_\mu\omega)_\nu dx^\mu\wedge dx^\nu$ without using coordinates Dec 14 answered Does $1^{\infty}=e$ or $1^{\infty}=1$? Dec 14 answered Partition into “fibers” $f^{-1}(y) \in Y$ Dec 13 comment Why vector field can be the gradient of a function $f$? To be clear, though, not every vector field on a Riemannian manifold can be written as the gradient of some function. Dec 13 comment Is there a reason for different nomenclature on Calculus of Variations? this is a great question; eagerly awaiting good answers Dec 12 awarded Favorite Question Dec 10 revised Let $f_1, f_2: \mathbb{R}^n \to \mathbb{R}$ be lower semicontinuous at $a \in \mathbb{R}^n$. Prove that $f_1+f_2$ is lower semicontinuous at $a$. added formatting