0
votes
0answers
4 views
fundamental class is the sum of simplices of triangulation of the manifold?
M is an n-dim closed orientable manifold.I find in a book"Intuitively,the fundamental class can be thought of as the sum of the (top-dimension)simplices of a suitable triangulation …
0
votes
1answer
162 views
Hartogs Theorem and Canonical Bundles
Let $X$ be a normal complex affine algebraic variety. Suppose that $Y$ is an open subvariety of $X$, and that the codimension of $X\setminus Y$ in $X$ is at least $2$. One version …
3
votes
1answer
111 views
The first eigenvalue of the Schrödinger operator is simple.
Hello,
let $(M,g)$ be a compact and connected Riemannian manifold (possibly with $\partial M\neq \emptyset$). We consider the Friedrichs extension of $L=-\Delta +V: C^{\infty}(M,\ …
1
vote
1answer
54 views
regularity of eigenfunctions of Schrödinger Operator
Hello,
I consider a compact and connected (smooth) Riemannian manofold $(M,g)$. I'm interested in the eigenfunctions of the Schrödinger Operator $L=-\Delta+ V$ acting on (smooth) …
-1
votes
2answers
204 views
Vector field pull back from embedding [closed]
Let $M$ and $N$ be finite dimensional smooth manifolds.
A smooth map $f: M \to N$ is an embedding if and only if there is an
open neighborhood $U$ of $f(M)$ in $N$ and a smooth ma …
3
votes
1answer
157 views
Closed geodesic loops around points in compact manifolds
Since in a compact Riemannian manifold $M$ the only totally convex subset is the whole manifold itself, see http://mathoverflow.net/questions/106169/closed-manifold-has-no-nontrivi …
0
votes
0answers
73 views
Differential form on a compact manifold whose exterior derivative is nowhere zero? [closed]
This may be a stupid question, but I understand the proof of the theorem that states that for any differentiable $(n-1)$ form $\omega$ on a compact $n$ dimensional manifold in $R^{ …
0
votes
0answers
41 views
Gradient estimates for subsolutions of elliptic equations
Let $M$ be a Riemannian manifold. Assume $u \in C^\infty(M)$ such that $u>0$ and
$\Delta u + \lambda u = 0,$
where $\lambda \geq 0$. There is a poinwise estimate for $|\nabla u|$ …
3
votes
1answer
260 views
Differentiable manifolds by Serge Lang question
I have started reading "Introduction to differentiable manifolds" by Serge Lang. In this book, Lang takes a different approach, by immediately introducing manifolds on arbitrary Ba …
1
vote
1answer
96 views
Vector fields on a simplicial manifold.
Is there a known definition of vector fields on a simplicial manifold?
For me, it seems natural that the definition should be something along the lines: Let $M_{\bullet}$ be a si …
1
vote
0answers
88 views
Topological classification of a real-valued functions on manifold
What is a motivation to study topological conjugacy of a real-valued functions on a manifold? (The importance of notion of a topologically conjugate homeomorphisms is clear for me) …
0
votes
1answer
200 views
locally symmetric space and global symmetric space
Let $Z$ be a compact, connected, orientable (Edit: as Misha point out) and locally Riemannian symmetric space. As a complete, simple connected, locally symmetric space is a global …
0
votes
0answers
62 views
Sobolev spaces on hypersurfaces
I am learning about Sobolev spaces on hypersurfaces.
Let $S$ be a $C^k$-hypersurface with boundary for some $k$.
In order to define a weak derivative, one needs $k \geq 2$ becaus …
1
vote
1answer
186 views
A “Riemannian” analogue of Kobayashi metric?
Recall that Kobayashi metric is defined on any complex manifold $M$. This is a pseudo-metric according to which a tangent vector $v$ at $P$ has length at most $1$ if there is hol …
1
vote
0answers
49 views
“Step-by-Step” toric resolution process?
WLOG the fan $\Sigma$ of our toric variety $X_{\Sigma}$ is simplicial. (So $X_{\Sigma}$ has at worst orbifold singularities and all cones $\sigma \in \Sigma$ are simplicial).
The …

