The specific star formation rate (sSFR) is commonly used to describe thelevel of galaxy star formation (SF) and to select quenched galaxies. However,being a relative measure of the young-to-old population, an ambiguity in itsinterpretation may arise because a small sSFR can be either because of asubstantial previous mass build up, or because SF is low. We show, using largesamples spanning 0 < z < 2, that the normalization of SFR by the physicalextent over which SF is taking place (i.e., SFR surface density,$\Sigma_{\mathrm{SFR}}$) overcomes this ambiguity. $\Sigma_{\mathrm{SFR}}$ hasa strong physical basis, being tied to the molecular gas density and theeffectiveness of stellar feedback, so we propose $\Sigma_{\mathrm{SFR}}$-M* asan important galaxy evolution diagram to complement (s)SFR-M* diagrams. Usingthe $\Sigma_{\mathrm{SFR}}$-M* diagram we confirm the Schiminovich et al.(2007) result that the level of SF along the main sequence today is only weaklymass dependent - high-mass galaxies, despite their redder colors, are as activeas blue, low-mass ones. At higher redshift, the slope of the"$\Sigma_{\mathrm{SFR}}$ main sequence" steepens, signaling the epoch of bulgebuild-up in massive galaxies. We also find that $\Sigma_{\mathrm{SFR}}$ basedon the optical isophotal radius more cleanly selects both the starbursting andthe spheroid-dominated (early-type) galaxies than sSFR. One implication of ouranalysis is that the assessment of the inside-out vs. outside-in quenchingscenarios should consider both sSFR and $\Sigma_{\mathrm{SFR}}$ radialprofiles, because ample SF may be present in bulges with low sSFR (red color).

Giant low-surface brightness (GLSB) galaxies are an extreme class of objectswith very faint and extended gas-rich disks. Malin 1 is the largest GLSB galaxyknown to date, but its formation is still poorly understood. We use VLT/MUSEIFU spectroscopic observations of Malin 1 to reveal, for the first time, thepresence of H$\alpha$ emission distributed across numerous regions along itsdisk, up to radial distances of $\sim$100 kpc. We made an estimate of the dustattenuation using the Balmer decrement and found that Malin 1 has a meanH$\alpha$ attenuation of 0.36 mag. We observe a steep decline in the starformation rate surface density ($\Sigma_{\rm SFR}$) within the inner 20 kpc,followed by a shallow decline in the extended disk. Similarly, the gas phasemetallicity we estimated shows a steep gradient in the inner 20 kpc, followedby a flattening of the metallicity in the extended disk with a relatively highvalue of $\sim$0.6 $Z_{\odot}$. We found that the normalized abundance gradientof the inner disk is similar to values found in normal galaxies but with anextreme value in the extended disk. A comparison of the star formation ratesurface density and gas surface density shows that, unlike normal disk galaxiesor other LSBs, Malin 1 exhibits a very low star formation efficiency. Owing tothe detection of emission lines over a large part of the disk of Malin 1, thiswork sheds light on the star formation processes in this unique galaxy,highlighting its extended star-forming disk, dust attenuation, almost flatmetallicity distribution in the outer disk, and exceptionally lowstar-formation efficiency. Our findings contribute to a more detailedunderstanding of the formation of the giant disk of Malin 1 and also constrainpossible proposed scenarios on the nature of GLSB galaxies in general.