Really, it is all about pixels and display resolution. The monitor size often means larger pixels, not more of them. I bought 4 HP2011x monitors that I intend to use in a rotated fashion. However, The standard back mounting are not present on the HP2011x nor can you rotate the monitor on the stand that comes with the monitor. The HP2011x is a poor choice if you are looking for a monitor you can use rotated in portrait orientation.
It's possible with proper adapters. The Apple Mini has a USB Lightening connection. The Hp monitor has only a 15 pin and a HDMI hook ups. You may be able to purchase a cable with the USB on one end and the 15 pin or HDMI on the other. But something tells me that you will need a conversion box that receive a USB on one side and a 15 pin on the other. In this case the hook ups you will need will be a USB to USB cable and a 15 pin to a 15 pin cable. Depending on the box (for the 15 pin), you will need to find out if you will need a double male end cable. USB's are interchangeable of course. To be honest, the technology is out there but it may be hard to find. I hope this information was helpful. Blessings Mellissa2010.
Update! Just found out that it does not have an HDMI connection.