Pilot flying reported another aircraft improperly landed close behind him; closed in at a rapid rate; and created an overall dangerous situation on the runway.

Narrative

I was operating my aircraft in the traffic pattern at Stearman Field (1K1). Winds favored landing Runway 35; and I made my first traffic call on CTAF at 4 miles north of the field with intentions to enter downwind for Runway 35 for a full-stop landing. There was no other traffic in the pattern; verified by radio; visual; and ADS-B returns. After calling downwind and abeam the midfield point; I noticed an aircraft moving rapidly from right to left (west to east); at my 1:00 position; about 2 - 3 miles from the airport and level with the 1K1 pattern altitude. As I made my base turn radio call; the aircraft proceeded to make an aggressive turn to the right (south); which was away from 1K1; and I completed my base-to-final turn. About the time I was in the flare for my full-stop landing; I heard an aircraft report 1-mile final on CTAF. As there had been no other aircraft in the pattern I was surprised to hear this call; but completed my landing and turned off at my normal taxiway approximately 4;000 ft. down the 5;100 ft. runway. While there were several other taxiways available to turn off; only one would not have required excessive braking; and that taxiway was only about 300 ft. prior to my runway exit. As I exited the runway; I glanced to the rear of my aircraft and saw Aircraft Y within 20 ft. behind me and following me off the runway. A person ; who was sitting outside of my hangar; reported that Aircraft Y landed closely behind me and closed on my aircraft rapidly enough that she thought there might be a collision.Upon shutdown; I exited my aircraft to see Aircraft Y on the taxiway immediately to my south and recognized the occupants. They proceeded to deplane as if nothing had happened; and I made it known that their aggressive actions had jeopardized safety. In a later conversation; the pilot flying initially asserted that by not exiting the runway early; I put him in danger as 'it was obvious you were going to taxi as slowly as possible; and you should have exited the runway out of courtesy.' As the conversation progressed; I told him that per 91.113; I had the right of way; and he then said; 'I lost you on the runway and by the time I saw you I was not in a safe position for a go-around.' Without regard to the decision to follow so closely on final; or not to elect a go-around; at some point both pilots in Aircraft Y saw my aircraft in front of them and elected to follow me so closely as to present a collision hazard in the event I needed to stop abruptly or experienced a brake or tire malfunction. Factors potentially contributing to this incident include:ATC handoff when transiting ICT Class C airspace from west to east; and late change to CTAF frequency; although Aircraft Y is equipped with two radios and most pilots will monitor CTAF and ADS-B when conducting these operations.Non-standard traffic pattern entry. The pilot of Aircraft Y executed a right 270-degree turn from base to final in order to 'lose altitude' but made the turn so aggressively that he put his aircraft too close to my landing aircraft to proceed safely. While the pilot asserts that he 'didn't see me;' he made the one-mile final call obviously to let me know he was right behind me and expected me to get out of his way.Poor judgement. The pilots in the Aircraft Y were in a position to execute a safe go-around at the one-mile call but elected to continue the landing; where they either 'lost sight' of my aircraft; or simply elected to get as close as possible behind me to make a point.Short of taking certificate action against aggressive pilots; the only possible solution to this is for all pilots to be aware of other aircraft operating at non-towered airports and be prepared to make a conservative and safe decision to yield to a closely following aircraft by electing to conduct a go-around to prevent an occurrence like this.