2020 mac mini work for display on 2011 imac

No, the new 2020 Mac Mini's do not support using any iMac including your 2011 iMac as a display.

Please carefully study > https://support.apple.com/en-us/HT204592

If you have or buy a new Mac Mini, then you will also need to get and use an external display.

see > https://support.apple.com/guide/mac-mini/connect-a-display-apd8e4fbbb97/mac

After the Mini is set up with a display or even a TV, you then could run it in what is generally referred to as headless mode. You would enable screen sharing on the Mini, then connect to it over a network with an iMac via Screen Sharing. Depending on your use, it may work well enough. Gaming or anything else graphics intensive would likely lag quite a bit.

Unfortunately, that configuration is not a supported option.

The new Mac mini cannot be used to host an iMac as a display. It is neither supported in hardware nor in the newer macOS software.