# Questions tagged [pushforward]

The tag has no usage guidance.

134 questions
Filter by
Sorted by
Tagged with
1 vote
18 views

### Uniform Continuity and Mass of Pushforward

Let $(X,d)$ be a metric space and $m$ be a regular Borel measure on $(X,d)$. Let $(Y,\rho)$ be another metric space and $f:X\rightarrow Y$ be a uniformly continuous function with increasing ...
1 vote
13 views

### Inverse push-forward on RKHS

I am considering an infinite dimensional separable RKHS $H$ of functions from $E$ to $\mathbb{R}$, where $E$ is any measurable space. I denote by $\phi:E \rightarrow H$ the canonical feature map of $H$...
38 views

82 views

### Push-forward of a smooth function

I'm confused about the relation between two concepts: the push-forward of a smooth map between two smooth manifolds and the differential of a smooth real-valued function. Let $M,N$ be smooth manifolds ...
37 views

26 views

1 vote
43 views

### Differential of a smooth covering map is always invertible?

If $f: E \to M$ is a smooth covering map between manifolds, is it true that the differential (or the push-forward) $df_p : T_p E \to T_{f(p)}M$ is invertible for every $p\in E$? I think this should be ...
139 views

I am trying to verify the following identity, where $M,N$ and $P$ are differentiable manifolds $\phi : M \rightarrow N$ and $\psi: N \rightarrow P$ are smooth maps between manifolds. Also, $f: P \... 4 votes 1 answer 132 views ### How to perform a push forward change of measure. Im a bit confused with the push forward formula https://en.wikipedia.org/wiki/Pushforward_measure Let$\rho$be a probability density associated to a probability measure$\mu$on$\mathbb{R}^d$, i.e &... 0 votes 0 answers 54 views ### Is$\phi_*X\in\mathfrak{X}(H)$left invariant if$X\in\mathfrak{X}(G)$is left invariant and$\phi\colon G\to H$is a Lie group homomorphism? Let$G$and$H$be Lie groups and let$\phi\colon G\to H$be a Lie group homomorphism. If$X\in\mathfrak{X}(G)$is left invariant, is$\phi_*X\in\mathfrak{X}(H)$(the pushforward of$X$under$\phi$) ... 2 votes 2 answers 177 views ### Confusion about pushforwards of Lie Brackets This is a very simple example that's bugging me, there's a basic gap in my understanding. Let$\gamma : [0,1]^2 \rightarrow M$be a curve, show that$[\frac{\partial \gamma}{\partial t}, \frac{\...
1 vote
Let $(M,g)$ be a metric manifold and $\phi:M\to N$ a diffeomorphism, where $N$ is another manifold. Let $\nabla$ be the Levi Civita connection with respect to the metric $g$, and we define a ...
Having some difficulty with the following proposition, Consider a $C^\infty$ map between manifolds $F:N \rightarrow M$ with $\text{dim} \, N = \text{dim} \, M$, then $F$ is locally invertible ...