Wired connection via HDMI cable is not possible.
To improve the performance, you can try any of these connection type (whatever is applicable in your setup):
– WiFi Direct/Wifi Hotspot (for Android/iOS/Windows client device)
– USB Tethering (for Android/iOS client device)
– Network Cable / crossover ethernet (for Windows client machine)
– Android Debug Bridge Cable (for Android client device)
For details, please check Performance tuning -> Network Bandwidth chapter in the user manual https://www.spacedesk.net/user-manual/.