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Learning Math
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0 votes
0 answers
22 views

For a proper Lie group $G$ acting on a complete Riemannian manifold $M$ by isometry, can we find $p'$ close to $p\in M, d(p,p')>d_{M/G}([p], [p'])?$

1 vote
1 answer
44 views

Isometric copy of the quotient $N$ embedded in the domain $M$ when $\pi:M\to N$ is a surjective Riemannian submersion?

1 vote
1 answer
44 views

Does a Riemannian submersion maps horizontal geodesics to geodesics, and a relevant question?

0 votes
0 answers
22 views

Is there a way to check that a given family $\mathcal{F}$ of continuous functions at $x_0$ is equicontinuous at $x_0?$

0 votes
0 answers
59 views

Continuity of the closest point on a closed, but non-compact submanifold $S$ w.r.t. the point outside $S$ we measure the distance

2 votes
1 answer
99 views

Why don't I see any mention of fundamental domain in the context of non-discrete Lie Group acting on Riemannian manifolds

1 vote
2 answers
153 views

Bound on expected norm of the difference between the sample mean $\bar{X_n}$ and population mean $\mu$ as a function of the sample size $n$ for LLN?

1 vote
1 answer
59 views

On the right inverse of a Borel measurable map between two Souslin spaces being Souslin measurable, i.e. mapping open sets back to analytic sets

2 votes
1 answer
97 views

Is it true that any sequence of random variables that converge in distribution is tight?

0 votes
1 answer
54 views

How to prove that this polynomial function of $m$ variables is strictly convex?

0 votes
0 answers
44 views

Is the gradient of following polynomial in two variables a local homeomorphism of $\mathbb{R}^2?$

0 votes
0 answers
91 views

Requirement of Hessian comparison theorem to prove that the squared distance function is strictly geodesically convex.

1 vote
1 answer
76 views

Replacing $o(1)$ by $o_P(1)$ while passing from deterministic to random

0 votes
0 answers
70 views

Obtaining uniformly tight sequence of random variables from uniformly tight sequences via polynomials: two questions

2 votes
1 answer
80 views

Is this following inequality with increasing powers of the components true for small $x$? And if yes, what's the positive constant $C?$

1 vote
1 answer
80 views

There's no way one can define the covariance matrix of just a probability measure without having a random variable, right? A paper did just that.

0 votes
2 answers
83 views

Relation between two normal charts on a Riemannian manifolds?

0 votes
1 answer
71 views

How unique is the orthogonal diagonalization of a real symmetric matrix, if we don't change the diagonal matrix of eigenvalues (no permutaiton)?

1 vote
0 answers
72 views

Must the first non-zero derivative in the Taylor expansion of a smooth function around its unique local minima be of even order?

0 votes
0 answers
110 views

Just checking: Hessian of the distance function on the constant curvature spaces are not of full rank?

0 votes
0 answers
206 views

On the calculation of the gradient of the squared distance function on a Riemannian manifold

4 votes
0 answers
233 views

Examples and characterizations of totally geodesic maps

2 votes
3 answers
256 views

Is the restriction of multivariate Gaussian PDF to one dimension a constant multiple of a one dimensional Gaussian PDF?

0 votes
1 answer
158 views

How to define the covariance of an inner product space valued random variable in a basis invariant way?

2 votes
1 answer
56 views

Why must a particular bijective linear operator on an $n$ - dimensional vector space satisfy a polynomial equation? (Without Cayley-Hamilton theorem)

1 vote
0 answers
75 views

Is it possible to have non-compact, embedded submanifold (without boundary) of a closed manifold?

1 vote
2 answers
97 views

Is the symmetric matrix $vv^{T} - hI$ is strictly negative definite for all small enough $h>0$? Is $\det(vv^{T} - hI)<0$ for small positive $h?$

2 votes
1 answer
207 views

How to define the expectation and covariance of a random variable taking values in an inner product space?

0 votes
1 answer
115 views

For a.e. $x$ in convex hull of $\{x_1\dots x_n\}\subset R^d, \sum_{i=1}^{n}(x-x_i)(x-x_i)^{T}$ nonsingular,$\{x_1, \dots x_n\}$ spans $R^d, n \ge d$?

0 votes
0 answers
71 views

Are the fixed points of a continuous map from a compact, convex subset of the Euclidean space to itself always isolated? If not, is there a condition?

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