User Laithy

7 votes

1 answer

532 views

Conformal Killing fields satisfy a third order PDE

asked Feb 14 at 20:04

6 votes

1 answer

296 views

Solving $\Delta \text{tr}(h) - \mathrm{div}(\mathrm{div}(h)) + \text{tr}(h) = f$ on $S^2$

asked Dec 14, 2021 at 5:49

6 votes

0 answers

124 views

Given the Ricci decays rapidly to 0 at infinity, is the metric asymptotically flat?

asked Jun 21, 2019 at 15:34

6 votes

2 answers

409 views

Existence and uniqueness of an Euler-type ODE with varying parameters

asked Aug 23, 2021 at 18:34

5 votes

1 answer

339 views

Finding vector fields on $S^2$ with equal divergence

asked Dec 15, 2021 at 1:48

4 votes

0 answers

146 views

Range of divergence operator on the space of traceless symmetric $(0,2)$ tensors; conformal vector fields on an arbitrary metric on $S^2$

asked Feb 22, 2021 at 17:19

3 votes

0 answers

96 views

A sequence of functions solving $-\Delta u_n + V u_n = u_{n-1}|_{\partial M}$

asked Aug 13, 2021 at 15:35

3 votes

1 answer

84 views

Existence and uniqueness of an Euler-type ODE with varying parameters part 2

asked Aug 24, 2021 at 17:21

3 votes

1 answer

163 views

$\Delta_g f = 0$ on the Riemannian Manifold $(\mathbb{R}^3 \setminus B , g)$ with conditions on the boundary and at infinity

asked Apr 22, 2019 at 14:41

3 votes

0 answers

198 views

Dirichlet to Neumann operator and the Riesz transform

asked Dec 3, 2020 at 22:29

3 votes

1 answer

146 views

Dirichlet to Neumann operator for a nonlocal ODE

asked Dec 13, 2021 at 4:31

3 votes

0 answers

159 views

Conformal Killing vector fields on manifolds that are not asymptotically flat

asked Dec 9, 2023 at 0:20

3 votes

1 answer

142 views

Estimating a solution to Euler-type ODE #2

asked May 2 at 2:39

2 votes

1 answer

142 views

Estimating a solution to an Euler-type ODE

asked Apr 26 at 19:54

2 votes

1 answer

226 views

The differentiability of the distance function on asymptotically flat manifolds

asked Mar 18, 2022 at 20:15

2 votes

0 answers

148 views

Finding an asymptotically flat manifold with ${\rm Ric}_{r\phi} = \frac{\sin\theta}{r^2}$

asked Apr 15, 2022 at 21:11

2 votes

0 answers

47 views

Growth/Decay of conformal Killing fields in cone metrics

asked Mar 12 at 23:14

2 votes

0 answers

138 views

Is $L^2([a,b]; L^2(S^2))$ the same as $L^2([a,b] \times S^2)$?

asked Apr 8 at 14:39

2 votes

0 answers

75 views

Regularity of solutions to an elliptic boundary value problem

asked Apr 24 at 21:26

2 votes

0 answers

141 views

For a 1-parameter family of metrics, how do we compute the derivative of the intrinsic geometrical objects like curvature, Hessian, etc

asked Dec 7, 2020 at 2:43

2 votes

0 answers

109 views

Finding $\Omega$ such that the 1-form $\Omega^2 \omega$ is $L^2$ orthogonal to conformal killing vector fields on $S^2$

asked Jan 8, 2021 at 17:33

2 votes

2 answers

159 views

Asymptotic Behaviour of Solutions to a Riccati-type ODE with Small Forcing Term

asked Apr 22, 2019 at 15:28

2 votes

1 answer

203 views

Given $Ric_g$ of 3-dim Riemannian manifold, induced metric $\gamma$ and mean curvature $tr_{\gamma}K$ on a hypersurface, do we have $K$?

asked Apr 30, 2019 at 17:42

2 votes

0 answers

269 views

Solvability of a PDE involving the Dirichlet-to-Neumann operator

asked Oct 31, 2020 at 18:59

2 votes

0 answers

229 views

Weighted Sobolev norm in terms of Spherical harmonics coefficients

asked Sep 20, 2021 at 21:13

2 votes

0 answers

127 views

Are metrics of the form $dr^2+ \Omega^2 r^2 g_\text{round}$ asymptotically flat?

asked Dec 5, 2021 at 15:29

2 votes

0 answers

100 views

Existence and uniqueness for $\Delta f + \lambda f = g$ on $S^2$ for $\lambda>0$ [closed]

asked Dec 10, 2021 at 19:02

1 vote

1 answer

182 views

Proving an estimate for the Neumann problem on $\mathbb{R}^3 \setminus B_1$ in Weighted Sobolev spaces

asked Oct 3, 2021 at 3:31

1 vote

0 answers

98 views

Two definitions of Sobolev spaces and the trace theorem

asked Oct 31, 2021 at 1:11

1 vote

0 answers

78 views

Trace theorem for $L^2([0,1]; H^k(S^2))$

asked Apr 25 at 16:33

Stack Exchange Network

33 Questions

Conformal Killing fields satisfy a third order PDE

Solving $\Delta \text{tr}(h) - \mathrm{div}(\mathrm{div}(h)) + \text{tr}(h) = f$ on $S^2$

Given the Ricci decays rapidly to 0 at infinity, is the metric asymptotically flat?

Existence and uniqueness of an Euler-type ODE with varying parameters

Finding vector fields on $S^2$ with equal divergence

Range of divergence operator on the space of traceless symmetric $(0,2)$ tensors; conformal vector fields on an arbitrary metric on $S^2$

A sequence of functions solving $-\Delta u_n + V u_n = u_{n-1}|_{\partial M}$

Existence and uniqueness of an Euler-type ODE with varying parameters part 2

$\Delta_g f = 0$ on the Riemannian Manifold $(\mathbb{R}^3 \setminus B , g)$ with conditions on the boundary and at infinity

Dirichlet to Neumann operator and the Riesz transform

Dirichlet to Neumann operator for a nonlocal ODE

Conformal Killing vector fields on manifolds that are not asymptotically flat

Estimating a solution to Euler-type ODE #2

Estimating a solution to an Euler-type ODE

The differentiability of the distance function on asymptotically flat manifolds

Finding an asymptotically flat manifold with ${\rm Ric}_{r\phi} = \frac{\sin\theta}{r^2}$

Growth/Decay of conformal Killing fields in cone metrics

Is $L^2([a,b]; L^2(S^2))$ the same as $L^2([a,b] \times S^2)$?

Regularity of solutions to an elliptic boundary value problem

For a 1-parameter family of metrics, how do we compute the derivative of the intrinsic geometrical objects like curvature, Hessian, etc

Finding $\Omega$ such that the 1-form $\Omega^2 \omega$ is $L^2$ orthogonal to conformal killing vector fields on $S^2$

Asymptotic Behaviour of Solutions to a Riccati-type ODE with Small Forcing Term

Given $Ric_g$ of 3-dim Riemannian manifold, induced metric $\gamma$ and mean curvature $tr_{\gamma}K$ on a hypersurface, do we have $K$?

Solvability of a PDE involving the Dirichlet-to-Neumann operator

Weighted Sobolev norm in terms of Spherical harmonics coefficients

Are metrics of the form $dr^2+ \Omega^2 r^2 g_\text{round}$ asymptotically flat?

Existence and uniqueness for $\Delta f + \lambda f = g$ on $S^2$ for $\lambda>0$ [closed]

Proving an estimate for the Neumann problem on $\mathbb{R}^3 \setminus B_1$ in Weighted Sobolev spaces

Two definitions of Sobolev spaces and the trace theorem

Trace theorem for $L^2([0,1]; H^k(S^2))$