All Questions
7 questions
5
votes
1
answer
243
views
Deformation of the Plücker coordinates
Let $M_{2,4}(\mathbb{R})$ be the set of real $2\times4$-matrices of rank $2$. For any $A\in M_{2,4}(\mathbb{R})$ and $1\leq i<j\leq 4$, let $p_{ij}$ be the corresponding $2\times 2$-minors of $A$. ...
- 93
5
votes
0
answers
104
views
On the embedding of manifolds into infinite-dimensional spaces
Let $X$ be a (connected, finitely dimensional) topological/smooth/complex manifold and let $i$ be a weakly continuous/continuous/smooth/holomorphic map from $X$ into the dual $F^{*}$ of a real or ...
- 5,529
2
votes
0
answers
179
views
Analytic continuation of $\int_V (f(x_1,\cdots,x_n))^s dx_i$
Let $V$ be an $n$-dimensional simplex, let $f(\boldsymbol{x}) = f(x_1,\cdots,x_n)\in \mathbb{C}[x_1,\cdots,x_n]$ be a product of linear polynomials that is non-zero in interior of $V$. Also let $E(\...
- 528
2
votes
0
answers
119
views
Covariant derivative of the Monge-Ampere equation on Kähler manifolds
I am reading D. Joyce book "Compact manifolds with special holonomy" and I have some problems of understanding some computation on page 111, the first line in the proof of Proposition 5.4.6. More ...
- 21
2
votes
0
answers
122
views
A parametrix for the $\bar\partial$ operator adapted to a holomorphic foliation
Let $X$ be a compact complex manifold with (regular) holomorphic foliation given by a holomorphic subbundle $\mathcal F$ of the tangent bundle. The foliation induces a filtration on differential forms....
- 51
1
vote
1
answer
191
views
Sequence of smooth maps converging to the identity [closed]
Let $\{g_{n}:B_{1}(0) \rightarrow \mathbb{R}^{2}\}_{n\in \mathbb{N}}$ be a sequence of smooth maps where $B_{1}(0)=\{x\in \mathbb{R}^{2} \mid |x|<1\}$ is the unit ball in $\mathbb{R}^{2}$. Assume ...
- 27
-1
votes
2
answers
129
views
Is it possible for all of the smooth/continuous curves in $R^3$ to form a Hilbert space? [closed]
Under which condition can it form a Hilbert space? Or what space can it form?
You can write down certain condition to make it to be a Hilbert space, e.g., Let $$p(t)=[x(t),y(t),z(t)]^T\in \text{R}^3$$ ...
- 11