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We present the serendipitous radio-continuum discovery of a likely Galactic supernova remnant (SNR) G305.4–2.2. This object displays a remarkable circular symmetry in shape, making it one of the most circular Galactic SNRs known. Nicknamed Teleios due to its symmetry, it was detected in the new Australian Square Kilometre Array Pathfinder (ASKAP) Evolutionary Map of the Universe (EMU) radio–continuum images with an angular size of 1 320
$^{\prime\prime}$
$\times$1 260
$^{\prime\prime}$ and PA = 0
$^\circ$. While there is a hint of possible H
$\alpha$ and gamma-ray emission, Teleios is exclusively seen at radio–continuum frequencies. Interestingly, Teleios is not only almost perfectly symmetric, but it also has one of the lowest surface brightnesses discovered among Galactic SNRs and a steep spectral index of 
$\alpha$=–0.6
$\pm$0.3. Our best estimates from Hi studies and the 
$\Sigma$–D relation place Teleios as a type Ia SNR at a distance of either 
$\sim$2.2 kpc (near-side) or 
$\sim$7.7 kpc (far-side). This indicates two possible scenarios, either a young (under 1 000 yr) or a somewhat older SNR (over 10 000 yr). With a corresponding diameter of 14/48 pc, our evolutionary studies place Teleios at the either early or late Sedov phase, depending on the distance/diameter estimate. However, our modelling also predicts X-ray emission, which we do not see in the present generation of eROSITA images. We also explored a type Iax explosion scenario that would point to a much closer distance of 
$\lt$1 kpc and Teleios size of only 
$\sim$3.3 pc, which would be similar to the only known type Iax remnant SN1181. Unfortunately, all examined scenarios have their challenges, and no definitive Supernova (SN) origin type can be established at this stage. Remarkably, Teleios has retained its symmetrical shape as it aged even to such a diameter, suggesting expansion into a rarefied and isotropic ambient medium. The low radio surface brightness and the lack of pronounced polarisation can be explained by a high level of ambient rotation measure (RM), with the largest RM being observed at Teleios’s centre.
Alexandrov’s estimate states that if 
$\Omega $ is a bounded open convex domain in 
$\mathbb {R}^n$ and 
$u:\bar \Omega \to \mathbb {R}$ is a convex solution of the Monge-Ampère equation 
$\det D^2 u = f$ that vanishes on 
$\partial \Omega $, then We establish a variety of improvements of this, depending on the geometry of 
$$\begin{align*}|u(x) - u(y)| \le \omega(|x-y|)(\int_\Omega f)^{1/n} \qquad \text{for }\omega(\delta) = C_n\,\text{diam}(\Omega)^{\frac{n-1}n} \delta^{1/n}. \end{align*}$$
$\partial \Omega $. For example, we show that if the curvature is bounded away from 
$0$, then the estimate remains valid if 
$\omega (\delta )$ is replaced by 
$C_\Omega \delta ^{\frac 12 + \frac 1{2n}}$. We determine the sharp constant 
$C_\Omega $ when 
$n=2$, and when 
$n\ge 3$ and 
$\partial \Omega $ is 
$C^2$, we determine the sharp asymptotics of the optimal modulus of continuity 
$\omega _\Omega (\delta )$ as 
$\delta \to 0$. For arbitrary convex domains, we characterize the scaling of the optimal modulus 
$\omega _\Omega $. Our results imply in particular that unless 
$\partial \Omega $ has a flat spot, 
$\omega _\Omega (\delta ) = o(\delta ^{1/n})$ as 
$\delta \to 0$, and under very mild nondegeneracy conditions, they yield the improved Hölder estimate, 
$\omega _\Omega (\delta ) \le C \delta ^\alpha $ for some 
$\alpha>1/n$.
